If the felt is glued on with hide glue, it might come loose with steam or hot water, but that might also damage or stain the felt. Depending on the age of the case, H&H guns have been around for a very long time, hide glue is probably the glue used. If it’s a newer case it’s more likely they used a more modern contact glue, which would be very difficult to remove without damaging the felt. I’m not sure if you have the gun that the case goes to, but like old firearms restoring them usually hurts their value. If there is a place that you can try the steam method that won’t detract from the whole, I’d try a small section to see if it works. Best of luck.