Quite a few ways to take up wear in a nut but if the screw is worn there isn't really a lot of use.
Square thread of 8 tpi means it has crests and spaces of 1/16" equally, second pic shows ? the spaces wider to the left of the nut ?
Hard to tell could be camera angle.

One alternative is to replace the screw and nut with a Myford ML7 part which is also 3/8" but 10 tpi acme to give 100 thou per rev