Hi Judy,
I’m afraid resin is a great adhesive. This is going to be a challenge.
First, have you tried breaking the cups off? You cup may crack, but at least it will be off your painting.
If that doesn’t work, try applying a heat gun or hair dryer to the area. Hopefully, that will soften the resin enough that you can peel your cup away.
If your painting is small enough, you might be able to try the freezer trick I have used for molds. Place everything in the freezer for 10 to 15 minutes, take it out, then slap the cups on a hard surface. With any luck, they will pop off.
Would you mind sharing what works for you?