When you cut circles to form your pierogi, there will be trimmings.
If you use a pierogi making tool, there will also be trimmings.
The proper handling of these trimmings is important.
If you mix the trimmings with a batch of dough that has not yet been rolled, you toughen that unrolled batch of dough. So if you are trying to make pierogi with a tender dough, keep your trimmings separated from any unrolled dough.
When all that you have left is trimmings, gathered them together, roll them into a ball and then roll out this mass as you normally would do to make pierogi.
This extra rolling causes a further development in the gluten in the dough and makes it tougher. Any flour that the dough picks up during this rolling process makes it dryer and also tougher.
Once rolled out you can make circles or use it on your pierogi making tool. Once again you will have trimmings.
If you are really concerned about the tenderness of your final product, separate this second run of pierogi that you make using the trimmings from those made from first run rolled out dough.
Serve your guests the first run, and save this second run for your family.
This final set of trimmings will be very tough when you roll it out again.
I do not throw this away. I simply roll it out, then cut it with my pizza cutter and make noodles. I use the noodles in soups.