Thanks for the advice - the difficulty in diagnosing this sort of problem is infuriating, given its particular nature and the challenge of describing the problem precisely, leaving aside the seeming randomness with which it occurs and the difficulty of replicating it in a controlled environment!
I don't think that the problem is with the way that our email gateways are set up, otherwise shouldn't it affect every email? And, since the carrier website has no problems (ie, that the incoming email has been correctly forwarded to the t-mobile instant email address), doesn't that suggest that the problem is synchronising the handheld with the instantemail inbox?
In case it is actually the email setup, then Outlook (not Web Access) is used throughout, and it's the firm's standard disclaimer (confidential, for the intended recipient only &c) that appears. If anybody else has experienced anything like this - with outgoing signatures appearing on incoming mail - I'd appreciate any help as to how to resolve it.