3 added 4 characters in body
source | link

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" - (12)

From Hiranyakeshin Grihya sutras prashna 1, Patala 4 section 13

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" -

From Hiranyakeshin Grihya sutras prashna 1, Patala 4 section 13

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" - (12)

From Hiranyakeshin Grihya sutras prashna 1, Patala 4 section 13

2 added 35 characters in body
source | link

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" -

Vajasaneyi Samhita IV.19From Hiranyakeshin Grihya sutras prashna 1,20 Patala 4 section 13

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" -

Vajasaneyi Samhita IV.19,20

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" -

From Hiranyakeshin Grihya sutras prashna 1, Patala 4 section 13

1
source | link

The Manu Smriti verse quoted in the question talks about situations where killing animals is sanctioned. One of them is Madhuparka.

There are several meanings to Madhuparka. Madhuparka is a rite during a marriage. The bride's family welcomes the bridegroom's family by giving a drink made of honey, curd or clarified butter. After this drink is offered, a ceremony was performed where animals are killed for feasting the party.

Ideal process for marriage is described in several grihya sutras. There are different grihya sutras which give different procedures but there are some common rituals. Ashvalayana Grihya sutras describe Madhuparka as an independent process whereas Manava Grihya Sutras describe this as a rite as a part of marriage ceremony. There is a difference of the ingredients in make Madhuparka.

Following is a process of giving madhuparka according to Ahvalayana grihya sutras. The sutras describe to whom it can be given.

  1. ṛtviks (priests officiating at sacrifices) when they are chosen for a sacrifice,

  2. A snātaka (a Vedic graduate),

  3. The king or a government official,
  4. One's ācārya (spiritual teacher)
  5. A bride-groom
  6. One’s father-in-law, paternal and maternal uncles or any other person who is dear to one and whom one wishes to honour.

Manu smriti not only mentions madhuparka as a situation where animals is allowed but also says how it should be performed.

rājartvigsnātakagurūn priyaśvaśuramātulān |
arhayen madhuparkeṇa parisaṃvatsarāt punaḥ || 119 ||

He should receive, with the “honey-mixture,” the king, the priest, the accomplished Student, the Teacher, the Son-in-law, the Father-in-law and the Maternal uncle,—coming again after a year.—(3.119)

Ashvalayana Grihya sutras Adhyaya 1 Khanda 24:

  1. He pours honey into curds,

  2. Or butter, if he can get no honey.

  3. A seat, the water for washing the feet, the Arghya water (i.e. perfumed water into which flowers have been thrown), the water for sipping, the honey-mixture, a cow: every one of these things they announce three times (to the guest).

.........

  1. Or (he may eat) the whole (Madhuparka).

  2. He then makes a rinsing of his mouth follow (on the eating of the Madhuparka) with the water destined thereto, with (the formula), 'Thou art the covering of Ambrosia.'

  3. With (the formula), 'Truth! Glory! Fortune! May fortune rest on me!'—a second time.

  4. When he has sipped water, they announce to him the cow.

  5. Having murmured, 'Destroyed is my sin; my sin is destroyed,' (he says,) 'Om, do it,' if he chooses to have her killed.

  6. Having murmured, 'The mother of the Rudras, the daughter of the Vasus' (Rig-veda VIII, 101, 15),

'Om, let her loose,' if he chooses to let her loose.

  1. Let the Madhuparka not be without flesh, without flesh

So, there are two cases here, if the bridegroom chooses to kill the cow, it is done. If not, the cow is set loose. Instead of cow, another animal is offered. Because Manava Grihya Sutras and the Ashvalayana above says there cannot be madhu parka without flesh. Hence, the sutra karas recommend alternatives like a Goat meat, Ram's meat is recommended. Bodhayana grihya sutras says (I.2.51-54) that when the cow is let off, the flesh of a goat or ram may be offered or some forest flesh (of a deer etc.) may be offered, as there can be no madhu-parka without flesh or if one is unable to offer flesh one may cook ground grains.

Bodhayana Grihya sutras Prashna 1 Adhyaya 2

tasyāmutsruṣṭāyāṃ meṣamajaṃ vā labhate |51|

āraṇayena vā māṃsena |52|

na tvevā māṃsorghyasyāt |53|

aśaktau piṣṭānnaṃ saṃsiddhayet |54|

As the cow became sacred, it became unthinkable to kill her and so other flesh was offered. When even flesh-eating came to be abhorred, then only payasā and such other things were recommended.

In the recent times, the practice of offering meat has abolished because of violence and other reasons. Cows became sacred. So, only payasā is offered. Ritual of killing cows and animals has stopped. Meat is never offered. This is only done for the name sake and a coconut is rolled up saying the same mantras and the bridegroom saying

" I say this to Rudra's mother, to the Vasu's daughter, to Aditya's sister, to the navel of immortality- to the one who understands: Do not kill the innocent cow, the Aditi, the knower of the speech who raises her voice.... Let loose the cow. Don’t kill this cow for me release her, let her drink water and eat grass!" -

Vajasaneyi Samhita IV.19,20