cordelli and cd1111:

These were the two solutions offered by my local luggage repair shop.

As they are somewhat low tech, and not very much effective, I was in hope that someone knows a chemical product that dissolves or dislodges the rubber from the fabric.

If chemically removing the rubber proves to be impossible, gluing or stitching a liner seems to be the better option, as removing by scrubbing probably will damage the fabric which, as an interior fabric, is not very thick.

Thank you for your suggestions; not knowing where else to ask, I'm in hope that a FTalker that works in the industry could, perhaps, offer a professional opinion.