If asked originally I would have told you to never remove it...
As noted in the protection phase post I put up earlier, you want to do everything you can to convey to him that
a. You WANT the marriage to WORK... but at b. You will NOT have ANYTHING to do wtih HIM until the affair is ENDED
These two points CAN appear to contradict each other... when you shut him out to reinforce b, it looks like you are saying a is NOT the case...
So, you have to make a clear verbal declaration that you WANT the marriage to work, and THEN you EXIT from his life until he ends things... THAT is the strategy...
However, if you see him every few days for child exchanges and such, and reply to his phone calls and texts, you really aren't combatting the affair according to this strategy.
Regarding the RING, it woudl fall under A and would help to convey that...
However, since you have alrady removed it, and he likley KNOWs this, you want to wait until its a meaningful time before you put it back on.
I would suggest at this point that you make a point of it NOT being on... And tell him you refuse to wear that while he's cheating on you... that way it becomes another pressure point forhim...
I would wait for others to comment, but that's my advice...
if you weren't doing NO CONTACT, I would suggest giving him the ring and the box it came in and telling him you don't want it back until she's gone... and walk away
BUT... you are in PROTECTION phase now and arne't going to have any contact with him.. RIGHT?... so that can't be done... so just keep it where it is for now in my opinion.
If it comes UP, tell him you are ashamed to wear that ring while he's in contact with her... DON'T get into a debate about wether he's cheating, just tell him you dont' want him anywhere near her and until she's gotten rid of, you are too ashamed of him to wear it.
Is tehre a way you can BLOCK texts from him on hte phone?
You need to do something about that phone... I would suggest you just turn it OFF.. it DOES have an OFF button.