Is it ok to pull my Piper Archer by the tail hook back into the hanger?
Does any one know if that will cause any damage?

It is probably ok provided you aren't pulling too hard. I see a lot of people
do it with winches in T hangars. On some Cessnas they actually tell you the
tensile strength of the rope or chain to use for tie downs. Not sure Piper
does but if they do then making sure you are not exceeding that strength should
give you no problems.

John Dupre'