Unfortunately there isn't a lot you can do into a 2mm? grout gap,you could possibly clear any grout remaining on the top and bottom only,then inject with a very fine nozzle some water proof silicon seal put as much as you can into the top,until it come out the side of the nozzle then when dry trim surplus off and leave as grout,try to leave the bottom so that the plaster that has been acting like a sponge ,will dry out hopefully, then do the bottom as the top, a hair drier may aid this process.HTH Tez