Some say it can be chanted without initiation and some say it can't be. Please resolve this query of mine.
In general, it is not recommended at all to chant any mantras without initiation. Please refer to this post for some verses.
Qualification (or Adhikara) of chanting mantras is obtained only after initiation.
Quoting from the article "Srividya Diksha Vivechini":
Srividya is a Shastra in itself and like every other Shastra, has the associated anubandha chatuShTaya – adhikAra, abhidheya, sambandha and prayojana. adhikAra describes the qualifications required to obtain initiation into shrIvidyA. Abhidheya is the subject matter of Srividya. Sambandha describes its relation with other Shastras. Prayojana describes the fruits obtained by studying Srividya. A guru should understand these four concepts well. As Srividya Shastra in essence advocates Nivrtti, it is also termed parA vidyA. Srividya is moksha Shastra or the science of liberation, which can be approached in five different levels, the upAsyas for which are lalitA, mahAtripurasundarI, rAjarAjeshwarI, parA bhattArikA and ahaMtA or sadakhyA. All these are generally termed as
shrI’. That Shastra which describesshrI’ is called shrIvidyA. Or, shrIyate sarvairiti shrIH – she who is worshipped by all is shrI.
As there is no difference between Brahma Jnana and Brahmi Bhava [brahmavidApnoti param], there is no difference between the upAsya [shrI] and it’s vidyA. Thus, Srividya refers to that vidyA or mantra which is of the form of shrI and refers to shrI. Also, as described in Siddha Yamala, Parashakti has two chief forms: Rakta Kali and Shyama Kali. Rakta Kali is called Vidya Rajni and Shyama is associated with Dakshina Kali and Sundari. Thus, Srividya refers to Sri + Vidya – Srividya, which encompasses the worship of both these forms and hence of Purna Parabrahma Shakti. Also, that vidya which has the ramA bIja as its core is referred to as Srividya. That which grants shrI i.e. purushartha chatushtaya is called Srividya. The term Srividya has been explained in 108 ways by Brahmasri Sri Tadepalli Veeraraghava Shastrigal.
In his book Japa Yoga, Swami Sivananda also advises against chanting Sri Vidya mantras without initiation.
Repetition of Subrahmanya-Mantra 'Om Sri Saravanabhavaya Namah' will give you success in any under taking and make you glorious. It will drive off evil influences and evil spirits. Repetition of Sri Hanuman-Mantra. 'Om Sri Hanumate Namah' will bestow victory and strength. Repetition of Panchadasakshara and Shodasakshara (Sri Vidya) will give you wealth, power, freedom, etc. It will give you whatever you want. You must learn this Vidya from a Guru alone.
Sri-Vidya is the great Mantra of Tripurasundari or Bhuvanesvari or Mahamaya. It is also called the Panchadasi or the Panchadasakshari, for it is formed of fifteen letters. In its developed form it consists of sixteen letters and is called Shodasi or the Shodasakshari. The aspirant should directly get initiation of this Mantra from a Guru, and should not start reading it for himself or doing Japa of it, of his own accord. This is a very powerful Mantra and, when it is not properly repeated, it may harm the Upasaka. So it is imperative that it should be got directly from a Guru who has got Siddhi of this Mantra.