In my experience (and I’m not saying it’s 100% correct), RMSD parcels are NEVER signed for by the postman and left. If the owner isn’t in then a card is left and proof of address has to be given at collection.

If it was only posted “signed for” then the postman will sometimes sign it himself.

From the above, I’d say that there’s probably more investigation required.
At this point I don’t think I’d be giving a refund unless you sent it “signed for” rather than RMSD.