I do the same but in this case I had already made the payment and they refused to give me an invoice without a contact number, and I didn't have any interest in a confrontation. If I had not made a payment I would have simply walked out.
If they refuse to give an invoice, tell them you’ll report them for GST evasion. [2]
[1]: https://www.onmanorama.com/news/india/2023/02/13/rajeev-chan...
[2]: https://theprint.in/economy/govt-launches-gst-reward-scheme-...