The whole portion of Taittiriya Samhita 18.104.22.168 is related to Soma Sacrifice and describing the rules of it in order to complete the sacrifice ritual only, according to procedure, so that the Yajamana and his wife may get the full benefits of the soma Yajna. As the success of these elaborate rituals largely depend upon accuracy of procedure.
Let us see what is the real context of the mantra and what is its meaning and purpose.
Some Background - As i said earlier the portion you quoted in the question is related to Soma sacrifice or Soma Yajnas. Which is either a single day or multiple day sacrifice. This sacrifice is consist of enthusiastically praising SOMA, a inspiriting drink from soma plant as god and king, because it gives a particular kind effect giving visionary Fluency, which can be seen in the mantras and hymns. i.e. Yajamana and Brahmanas can clearly can experience the power and can see the real meaning of mantras and hymns.
The procedure of this sacrifice involves pressing the Soma plant and preparing a drink to be offered to various gods. This soma plant is pressed three times. These pressings are called Pratha Savana (Early-morning Pressing),Madhyandina Savana (Midday Pressing) and Tritya Savana.
During the first two pressing the wife of Yajamana is not present there at pressing. But interestingly at the third pressing she has to be present. While the first two pressings are of fresh soma plant, the third one is repress of the residues, which is acquired from two previous pressing.
After offering the soma juice to gods, during the third pressing the residual leftovers is again pressed and a weak drink is prepared, which is then mix either with curd, milk or ghee for human consumption. But even after pressing the soma plant for two times, it was observed that the even residual soma plant leftover if repressed again can give the same kind of effect as the freshly pressed soma juice.
The mixing of leftovers and the mixture's ritual usage is thus a complete ritual.
And the actual purpose of the mantra is to tell us that Women (wife of Yajamana) is not fit to receive the share of this soma drink and to barred them from taking it.
And the mantra is just explaning us the causes of why women are not allowed to take share of soma Drink.
Now lets see the wrong translation given by the author and see the actual meaning.
Women are powerless, have no inheritance, and speak more humbly than
even a bad man."
1) Women are powerless - Women (wife of the host) is
not strong enough to press this soma plant because its particularly
tough plant to press by hand.
2) have no inheritance - Women are not the
priests by inheritance (only priests and yajamana are allowed to
take the share) and Women are not allowed to perform this Yajna
alone (without her husband) , because these Yajnas are costly and
husband can only afford the sacrifice, so they are unfit to take the
share of soma juice.
3) speak more humbly than even a bad man - Soma
is strong drink, women especially do not like the taste of it and are
not capable to resist it's strong intoxicating effect. And if
they are allowed there can be adverse effects of the drink on their
health. So they are barred from taking the share of the soma drink
as it is in Soma Yajnas.
What you have quoted is missing the soul of the mantra, its actual purpose and is wrong translation.
Note - The some portion and info. in this answer is compiled from various discrete sources from the internet. So considered this as partially sourced or unsourced answer. I have tried the honest effort to state the correct info. in the answer as much as possible I will update the answer if more strong evidences are found , as there is no reliable english translation of Taittiriya Samhita (by indian author) is available widely. Here is one of the sources .