New [old] uke day

bought this Gretsch soprano off FM and it arrived today. Very pleased with it. very similar sound [and look] as a Martin 0. built very lightly and has great sustain. I knew it had some serious flaws when bought it but what was described as a quarter sized hole turned out to be the an area about 2" x 4" that was bashed in and the repair leaves something to be desired. some sort of stain was applied to the back so the grain barely shows through. then a finish was applied poorly, so it resembles alligator skin, lot of small bumps
my question is should I leave it alone? sand the finish off and apply a new one. maybe something easy for an amateur like tru or tung oil? the top has such a pretty grain it's a shame about the stain. the stain may have been mixed with the finish and applied together. any suggestions.?

Since the back finish is not original, there no reason not to correct it.
Did the refinish get into the crack? If not I would work on repairing the crack first. Then it will be easier to sand and refinish.

Maybe you want to see a luthier on that repair. It is definitely not quarter sized.