Since the photo shows the string is still there, I would try first to push the string so if possible pull it from the inside, then clip cut it so there is no string piece at all in the peg.
That's because the string applies pressure from the inside of the peg, by expanding it.
Once so, it should be easier to get the peg out, first pushing it out from the inside.
If even so can not be pushed from inside, the next thing might be to drive as slow speed a small diameter drill using the string hole in the peg as a guide. Do not use any drill even close to the diameter of the peg. Step up in drill sizes. Once the peg wall is reduced, it weakens and should easily come out.
I wouldn't use a dremmel, because of its high speed, even to drive a drill bit, for that case.
Also, once you have drilled a certain size, you could then, by hand drive a small diameter screw (only enough turns to grab the peg, not tight), and THEN use pliers to grab the head of the screw and pull peg and screw out together.