I have not used aluminum jelly, but have used lemon juice many times on buttons with a bunch of gilt left. However, I am fairly certain the relic hunters who advoacte Aluminum jelly do not use it on buttons without a lot of gilt being exposed. I believe it is not too kind to just the normal brass/copper button.
So, either try Peroxide or go slower with warm water soak, and cotton swaps to try and removed encrustations. I cannot tell from the photo how it would end up, I have so many of those types I would not be too concerned about the outcome. Sometimes removing the encrustation exposes how badly corroded it is underneath and the detail was only there due to the encrustation, but it is up to you. You can also just dry brush it alot with an old toothbrush and let it be. Your button, your choice.
I believe buttons with backmarks like that are no earlier than early 1800's up into the 1830's.
Don