Bought second hand and it arrived slightly tacky. Salvageable?

Took a chance on a used piece because the price was good and I could not have afforded anything similar new. It arrived today and the surface feels very slightly sticky, especially on the inside.

It looks alright otherwise. Good colour, no marks I can see, seams all intact as far as I can tell. The seller described it as barely worn and I have no reason to think that was untrue, just that it has probably been sitting in a drawer for a long time.

Is this fixable, or have I bought a nice looking piece of rubber that is already on the way out? And is there anything I should check before I try to put it on.