Gatiss makes it clear that its a prop rather than people think it is his own ring.

However it has been noted elsewhere that Anthea also wears a similar ring on the same finger. Possibly just pure speculation as there's no reference to Mycroft being involved in any secret societies or lodges etc etc nor would he need to be really.

I think it was discussed more to allay speculation that there's more to it; which like every other syllable uttered by Gatiss & Moffatt has probably been twisted into wild theories already .
lol

Why have Mrs Hudson trying to carry on an affair with the guy from the deli?
Why have Sherlock eat from Mrs Hudson's fridge at will?
Why does Sherlock wear a scarf & coat?

It's just something to round out the character. In most scenes nearly everything you see is a specific prop, someone has decided what goes in the scene and what goes. The ring, the shoes people wear , etc would all be no different.

Funnily enough it does spark conversations in another area but I will leave that alone.

Well, if it's true that the ring Anthea wears is identical to Mycroft's (I haven't noticed), seems we should all be looking for similar rings on other characters' fingers (i.e., the people that swarm to Sherlock's "body", etc.). Something to keep us busy during hiatus, anyway.