It's not pedantry, MR. It's a matter of fact.
I know it has been so for as long as I can recall. I vividly remember,when I took a passing interest in such matters, David Coleman almost losing his voice when shouting "It's [David] Hemery Great Britain, Hemery Great Britain" as the runner powered to the UK's only athletic gold medal in the 400m hurdles at the 1968 Games.
But I, too,do not understand why it should be "Team GB". I have heard all sorts of explanations, the most credible of which seems to suggest that when GB registered its entry to the first modern games in 1896 Ireland (in its entirety) did not exist as a nation in its own right and was part of Great Britain. However, things move on and the Olympic movement has had plenty of changes to accommodate so it should not be beyond its wits to sort out this matter which must have been a problem since 1922.
I understand the (UK) government wanted the team referred to as "Team GB and Northern Ireland" (which had been attempted at earlier games) but it is not difficult to understand why it did not catch on. Apparently competitors from Northern Ireland can (for some unfathomable reason) choose to participate for either "Team GB" or Ireland. However, in my view, if they opt to take part under the Union Flag then they should expect to form part of the team of the United Kingdom.
Of course this problem may not have been quite so insoluble had not the ridiculous title "Team GB" gained a hold. No other nation seems compelled to entitle its team in such a way and if we reverted simply to "United Kingdom" or even "UK" for those challenged by multiple syllables the problem may be satisfactorily solved.