I have only encountered the TP as meaning Temporary Packaging (the document quoted by Allan). As for the "5" on the tin I don't know what that refers to, although no doubt in some documentation it may indicate the type and mark of the igniter set; the fuze burn times were nominal 4 or 7 seconds depending on use as hand or rifle grenade.
What is ironic about the problem of the circular wooden packing piece is that this very same occurred in WWI.
From the Royal Commission on Awards to Inventors, Mr FW Vickery's Claim "Transport Box and Mill Board Holder for Mills Grenades", July 1919, Vickery's Counsel said: "The second claim in this case is in respect of a design for holding those metal fuses, because the original design included the use of wood, and the wood, owing to the sap and natural moisture, had a way of injuring in some way the metal fuses, which caused trouble; it caused the fuses not to go off..."
Vickery's solution was the use of perforated mill board spacers, which apart from solving the problem of moisture damage to the igniters also saved a lot of money over a run of 4 million boxes. It would appear the lesson from WWI was not heeded in WWII.
Tom.