Hi Angela,
You are in for a challenge.
The first thing I would try is to get boiling hot water on the area inside your mug. With any luck, the resin will soften enough that you can scrape or peel it off the stainless. If it’s not in an area where you can easily get hot water to stay, place a rag on the area first. Apply the hot water to the rag.
If that doesn’t work, the other thing you can try is to use methylene chloride to remove the resin. This agent will dissolve resin and let it pull away from the metal. Please know, this chemical is very dangerous. If you are going to use it, follow all safety precautions!