I would try a 'Dental Pick' and take small bits at a time. Also might try heating it slightly with a heat gun or hair dryer. Since it is a form a rubber it should soften a bit. Just don't get to hot and distort the resin casting.
Were you molding a resin piece or pouring up a resin piece?
If you were molding a resin piece, you should dust it with a coat of crystal clear or a mold release next time.
If you were casting a resin piece, there are several possibilities.
1 - If it was a new silicone mold, many RTVs will stick to resin if used to quickly after being made. You really need to wait a good solid day before attempting to pour up a resin piece (to be on the safe side).
2 - If it was an old silicone mold, believe it or not, urethane resins are one of the most volatile things that can be used with silicone. They actually attack the rubber from the very first pull. The isocyanates help to draw out the oils from the rubber (among other things) and can stick for that reason. Therefore, you want to use a release to help. Some releases actually attack the silicone over time as well, so yoo might try a spray release coating, allow that to dry, and then powder the mold with baby powder/talc. You shouldn't need to use any additional release for at least 10 pulls (depending on the complexity of the part).
3 - If you're using an old resin, it's possible that it generated a higher than normal amount of heat during the curing process which "ate through" any releasing ability of the rubber.
The possibilities are numerous unfortunately.
Something you can try that does work in many instances is to try to saturate the bonded area with Isopropyl Alcohol. This usually works quite well...