Gretsch was a large US mainland producer of musical instruments including ukuleles. They were founded in 1883 in New York by Friedrich Gretsch and remained in the Gretsch family until 1967, (at this point they had definitely stopped making Ukuleles), usually under a Fred Gretsch, (between 1942 and 1947 Fred the thirds brother Bill was in charge). In 1967 the company was sold to Baldwin Music but in 1985 Fred W Gretsch (Fred IV) brought it back and moved it to Savannah Ga. 

In addition to selling their own products under the Gretsch or Gretsch American name, (starting 1926),  they used Clarophone as a brand name on Banjoleles and Kaholas & Co. on Ukuleles, (I believe it is the case that in the late teens/early twenties they brought unbranded Ukuleles from one of the Hawaiian makers, or possibly Leonardo Nunes, (which is why the Kaholas labels also say "Ukulele'O' Hawaii"), and put the Kaholas label in, later they decided it was easier to make the Ukuleles themselves. Rex on Guitars, Mandolins and other fretted instruments, Broadkaster on Drums and some Banjos, plus they also made all sorts of instruments including Ukuleles and Banjoleles to be branded by others like Bruno, PMICo and famously Montgomery Ward with their Sherwood line.

In 2012 Gretsch restarted selling ukuleles and banjoleles, (I have read there is some kind of deal with Fender but I'm not sure of the details?) calling them part of the Gretsch Roots Collection. The first range consisted of an open back Banjolele branded Claraphone and Soprano, Concert and Tenor Ukuleles in laminate or solid mahogany, (made in China). In 2013 they expanded it with the addition of a wood bodied Resonator, a Guitalele and a reissue of the famous blueburst Roundbody Soprano for a limited run. Prior to the re-introduction there were some prototypes released featuring the vaguely triangular soundholes found on Gretsch acoustic Guitars. exactly when and how many I don't know