How do I remove old, glued on pick guard without damage or can I polish it somehow and make it look better. I looks like hell right now.
Hair dryer, heat the glue gently until it starts to melt.

Or just trace it and cut a new pickguard
Why is the pickguard glued?
2002 PRS CE22
2013 G&L ASAT Deluxe
2009 Epiphone G-400 (SH-4)
Marshall JCM2000 DSL100
Krank 1980 Jr 20watt
Krank Rev 4x12 (eminence V12)
GFS Greenie/Digitech Bad Monkey
Morley Bad Horsie 2
MXR Smart Gate
Acoustic guitar? In which case it's not glue so much as it is a double-sided adhesive film.
If it's just scratched (not really deeply) then you can do what I did on one of mine. Use very fine wet and dry paper (wet) to get rid of the really deep scratches, then work to finer and finer papers until most of the scratches are out. Next use rubbing compound to get rid of these scratches- note the scratches from rougher grades must be gone. This will get the pickguard looking pretty good, but you may then need to polish it afterwards (with wax or something) to get it really shiny. Make sure you mask off any other areas very carefully as you don't want to scratch/ get rubbing compound on them. May be easier to take it off first.