Well the rifle looks like a legit TR rifle after all, with a replaced forend and buttstock. The scope and mount legit Because the rifle lacks the T mark, it would appear it was not mated with a scope at Holland and Holland.
I expect the rest of the story will likely be explained by Captain Laidler, as he was in service working on No4 T around the time that the armorer's tag says this rifle was worked on. Very neat set up.