I know we have to be purify before making salah and praising Allah swt. But how's a woman supposed to make supplications to Allah swt if she's on her menses and not purify.
First of all note if all of us needed to be purified to perform dhikr or du'a logically that would mean that women would have a vast disadvantage, only because of something Allah created:
They have menses and they have the postpartum period which are long periods of time where they would not be allowed to communicate with Allah, while men can only become impure due to intercourse or janabah which they share with women too.
I think only from a logical view this can't be, as Allah would never "reject" people (as du'a or dhikr means asking Allah and remembering HIM) for something HE has created HIMSELF!
Therefore purity has only been prescribed for the prayer itself by the Quran (Note that this is the only kind of worhsip women don't need to make up due to menses or postpartum period, while they need to make up fast and tawaf etc.).
So here's a fatwa on the Issue of your question.
Note that a women in menses can do the following worships:
- She can read any book which has some verses of the Quran inside (as long as it is not a Quran) note that this already is dhikr (remembrance of Allah).
- She can listen to quranic recitation or recite from her memory (See fatwa in Arabic).
- She can even prostrate if she passes by a Verse of prostration (See fatwa in Arabic)!
- She can recite any dhikr (see fatwa in Arabic)!
- Some scholars allow it to read from a Mushaf (copy of the Quran) if there's something between her hands and the Mushaf (see this fatwa in Arabic), so if somebody put it on a desk and she reads from it without touching that also would be allowed (see also this fatwa)!
- She can also attend the Khotba of Eid and attend the EId prayer without participating in it (see in sahih Muslim).
See also this fatwa on what a woman in her menses can do during lailat al-qadr!
I also forgot to mention that non-Muslims perform dua' and you may even find quotes in the Quran of disbelievers asking Allah, which underlines that purity (tahara) is not a condition for performing dua'.
And Allah knows best!