Dealing with peeling sealant on marble countertops

I'm going to preface this by saying that I am a new, first time homeowner so a lot of my questions might seem a bit basic but I am in my first forays in dealing with this type of thing. Hopefully that means my questions are easy to answer.

So upon moving into the new house I noticed that there is a peeling, clear residue on the dark marble countertops (I should have noticed this before buying, but frankly I would have bought anyways). Based on my google-searching so far, I'm guessing that it's peeling sealant that the previous owner used (there might be some amount of normal kitchen-grossness-residue, but I don't think that's mainly it).

I'm trying to figure out how to handle this. Do I sand it off, or is there some sort of solvent I can use? I assume I'll be resealing it once I have the old peeling gunk cleared off, but I'm not sure what the best way to do that without damaging the marble underneath is.

Thanks!

Dealing with peeling sealant on marble countertops