Yes, no "T" was stamped on the receiver side wall. As far as I know, the letter "T" was, in general, stamped by Holland & Holland after matching the scope with the rifle. H. & H. has no connection with the "ItalianLee-Enfield sniper rifles", so nothing "T".
The Scopes: I think they are almost all, No. 32 Mk I reworked here, for this reason, I think, they maintein the slide shade. Italy also used the Mk III scopes (but not on these snipers) without adding the slide shade.