Greener marked and retailed Lee Sporters with their name as did many other firms.
BSA made most of the commercial sporters,,LSA made a few also.

I don't recall Greener as a mfg'r of Military SMLE's at all. They might have sporterized a few after the war and sold them. Seems like most anything was done to make some money then.

The Lee Sporters were made on Lee Metford and Lee Enfield (Long Lee) actions. Though BSA did offer commercial versions of the Mk1* (SMLE) rifle for civilian sales.

The sporters could be had in several versions, some of a more military flavor with names like Officers Carbine and such.
The sporting rifles commonly thought of as the Lee/Speed rifles were the top of the line. Available in 3 grades IIRC and a number of options and 4 calibers. Probably more if you asked (and paid).
These were all commercial rifles, not redone X-military pieces.