It is not always a question of wanting to make a change through a different company than the one that issued the ticket. For whatever reason, my TA books *A RTW tickets through TG, but TG doesn't seem to know how to make a change to the ticket once you have finished your flights with them.

You certainly don't want to do that - lucky you if you don't have to! In one of my previous posts I explained which scenario works best (have one travel agent or one airline book and ticket everything and stick to them for rebookings and ticket revalidations and/or reissues). That's what you did (book everything with LH and change everything with LH) and it worked fine because they have the big picture on their screen.

The problems people are writing about in this thread arise from having to do it differently. Let's assume you are at the other end of the world and can't reach your travel agent or issuing airline because their office is closed, they don't have a local phone number in the remote country your stuck, or you simply want to change one small part of your itinerary and call the operating airline directly thinking that this is the most direct and easiest way to rebook. This will almost certainly lead to big trouble with the rest of your itinerary. Bottom line: Never, ever let anyone touch your RTW reservation or your RTW ticket except for the TA or airline who booked and ticketed it, even if that means going through some hassles to contact them.