The TSM accounting records.
If you turn accounting on, TSM will cut one record for each session the
client starts.

The record gives you a count of the "objects" restored and the KB restored
during the session.  "Objects" include files+directories+any other things
TSM considers "objects", which makes it a little difficult to come up with
an exact file count, but you get a good idea of who is doing what.  Just
knowing the number of sessions that do restores may be all you need to find
out.

The accounting record fields are described in the admin guide.