Yardrat Memory does not prohibit saving locations inside of a TMQ on the new client, yet it does on the old client. It is also worth noting that if a player attempts to teleport to this saved TMQ location, their character will simply bug out and go invisible/unable to move, so they will have to relog to fix it - where they will respawn at their Popo Stone.
----
Here is a comparison:
It says 'can't teleport' when a player tries to save a location; so stops them from doing so.
Within the New client, there is no error message and the player can save the location - despite it bugging them out if they try to teleport to it.