That's a Gretsch "Name Band" model. Gretsch usually don't have re-rings, they came up with the modern staggered seam shell design that didn't need them to keep the drum round. The throw off is a Micro Sensitive and the adjustable tension on the butt side is correct.
I wouldn't re-wrap it unless absolutely necessary. If necessary use Jammin' Sam's sky blue pearl which is close to the original color this drum was. But it's probably worth more as is than it would be re-wrapped.
http://www.jamminsam.com/vintage-sky...-drums-page-2/
$25 was a heck of a steal. The badge on the drum is worth 3 times that by itself.
Does the throw off work? If not it can be fixed.