[TonyJSenior]

Nope not the pawl spring - it's the larger gear behind the dial assembly that ultimately drives the tuning cap. I don't see the part on the 3 PDF's, but you can see the gears depicted somewhat on the first illustration you reference from the Mallory-Yaxley document. Just looked at vintage-electronics.com and found a similar part shown as "Philco 37-116 Tuning Assembly Part - Vernier drive GEAR". If you search for that part, it should pop up with a picture. On the 38-7, I don't believe the springs contact anything whatsoever and can't imagine that the gear "twists" out of shape requiring them. But then again I'm no mechanical engineer either