Leeward Mark

I think there's a specific confusion about right of way in the OP.
These days right of way is a specific thing covered by rules Rules 10 to 13. The later rules then put restrictions on what the ROW boat can do.

In the original post we don't absolutely know which boat has right of way, but its a pretty safe guess that if its a gybe mark then the boats are on the same tack, the one on the outside is windward boat, so the boat on the inside is leeward boat and has ROW. This doesn't change until they change tack.

An entitlement to mark room does not give right of way. It means that even if the other boat has ROW it is limited in what it can do because it must give room.

In this case it all follows as Brass says. Inside may luff up but not tack, and may not sail beyond the mark without gybing. So if A wants to go beyond the mark and tack round she needs to plan early, slow down and let B go ahead.

I stand corrected. But, in the second part of your answer you say "A is not entitled to room to tack." which is basically what I said (accepting that my reasoning may have been flawed)?

Boats with rights to mark room are only entitled to enough to perform "a seamanlike rounding" not a tactical rounding. I'd say he is only entitled to room to gybe on the basis that if it's not too windy to race it's not to windy for a competent crew to gybe. Pragmatically, if he's going to chuck it in right across your bow I'd give him all the room he needs, even slowing down to let him pass you before you gybe. How do you know he wants to wear round?