I'd clean the mortice where the plate touches around the edges,scrape and de-natured alcohol,poke a couple of holeson that edge,roll thin ribbon's of "Quick wood" a tube of 2 part epoxy that you cut a slice off of,nead together untill a uniform color,grease the lock plate,press the epoxy putty into the edge,making sure the putty gets into the little holes,then press the plate into the mortice,install the screw and just finger tighten it,then let it set untill the putty set's up and then some. if any squishes out you can remove the excess with a putty knife,then run a rag with de-natured around the plate before it sets up. That will cure the issue.