Will the tape eventually wear off?

I put down some rugs through our kitchen to help our old dog out. I secured them with carpet tape.
Well her problem walking seems to have improved greatly BUT she’s been peeing on the rugs off and on. It’s gross! I finally decided to pull them up.
I’m having a murderous time getting some of the tape up. I’ve tried Goo Gone and other things.
I’m honestly ready to give up. Will what is left gradually wear off over time?