With any restringing job completed the price includes replacement damper felt. Along with all of the dirt and oils collected by the felt over years of service, the original felt work will be worn in a particular pattern that would not fit well over the new strings. I find it best to install new felt so the new wire can form its own pattern in fresh materials.
Replacement damper felt can be found in bulk or in pre-cuts; either way is a satisfactory replacement. Some times when replacing felt work one can discover a cut or length of felt that is not offered by the supply house standard pre-cuts.
There are several felt guillotines sold by the piano supply houses, and all of them do the job of custom cut felt in much the same way. I use the guillotine quite a bit as I make my own backing felts at times out of non- traditional reds and other colours.
Once the replacement felts are ready for install they are glued into place with hot hide glue. After 24 hours the dampers are ready to be reinstalled into the piano. Because the damper wires were marked with a scribe previous to removal the installation goes quite rapidly.
Here are some photos of the damper replacement process and one of the felt cutters.
Same photo album starting at photo 118
Replacement Damper Felt