Without having seen it… I’d say a simple adhesive. I’d go with a dab of silicone if you know for certain it will not bleed out over to the felt side.
Would not need much at all. The silicone will also take the vibration without falling out. Did this in a vintage Charger a long time ago. Worked like a charm.
If it is the felt itself…. ie… cloth…. try some double face tape. You’d have to fine something very thin, but that should work.
