Do the clothes worn by a mestruating woman need to be washed even if
they are not stained by the menstrual blood? Once her periods have
finished, can a woman perform salat with the clothes that she wore while
menstruating without washing them if they were not stained with the
Praise be to Allaah.
So long as the clothes she is wearing do not contain any najaasah (impure substance), she is permitted to pray in them, even if she was wearing them during her monthly period. The menstruating woman herself is not naajis, neither is her sweat. The Jews used to think this, but Allaah stated that this was a lie, as is reported in the saheeh hadeeth narrated by Muslim (may Allaah have mercy on him) from Anas:
"When one of their women menstruated, the Jews would not eat with her or sit with her in their houses. The Companions of the Prophet (Peace & Blessings of Allaah be upon Him) asked the Prophet (Peace & Blessings of Allaah be upon Him) about this, and Allaah revealed the words (interpretation of the meaning): ‘They ask you about menstruation. Say: That is an adhaa (a harmful thing for a husband to have intercourse with his wife while she is having her menses), therefore keep away from women during menses and go not unto them till they have purified (from menses and taken a bath)…’ [al-Baqarah 2:222].
The Prophet (Peace & Blessings of Allaah be upon Him) said: ‘Do everything except have intercourse.’ Word of this reached the Jews and they said: ‘What does this man mean, in every issue he differs from us!’" (Saheeh Muslim, 455).
If the clothes get some menstrual blood on them, it is enough to remove the impurity with water and then she can pray in them. And Allah knows best.