What it is is just the carbon lining some pipe makers use to protect the pipe during the break in process, whether or really works or not is up for debate and pipes do not need them at all, I would just try to put it back in place with my finger or rip it off and keep puffing away. When that layer comes cracked is when I start to worry. You could always use sandpaper and remove it all from the inside of the pipe, but that is very time consuming. The black carbon layer will eventually burn away, so you shouldn't worry about it too much.
These layers should never come off with a tamper, sounds more like it wasn't applied correctly, which isn't a big problem, more of an aggravation. Unless it was a super expensive pipe, I would just let it go and enjoy smoking it as is, cracks in the wood are really what you should be on the lookout for and just don't puff away on it more than you need to at the start, if it feels too hot to hold, you need to set it down and resume puffing when it cools down a bit. Have fun, welcome to the forums