It probably won't hurt normal glasses.

H2O2 is great for attacking organics (finger prints, grease, oil), but at 2% it's probably not going to do much for visible smudges. But most chemical labs use 30% H2O2 solutions (it is a very aggressive oxidizer).

Peter's comments about damaging AR coatings is worth keeping in mind. I believe that when people at work clean delicate optics they use generally straight ethanol + lens paper. Stronger solvents can be risky, and in general solvents shouldn't be used with plastic lenses.

https://www.newport.com/n/how-to-clean-optics

I use liquid "soap" or dish detergent on my glasses (AR coatings and the whole nine yards) - seems fine. Lots of water to rinse.

Cheers,
Scott.