Since Elly is as dumb as a sack of hair, it's quite likely that she doesn't understand that the same blasted thing might have been going on with that cedar chest Thelma gave her. What could easily have happened is that Thelma reflected on what her nieces and nephews were up to and thought to herself "Gee willy-wonkers!! Dora and Wesley are fit to murder one another over that old chest of mine! Maybe if I hand it off to that dozy idiot woman who I used to live next to because I feel sorry for her and her family, they'll settle the heck down!!"
The reason that she might have been seen as a useful neutral party that Thelma almost pitied would never actually occur to the poor, dim-brained creature is, of course, the fact that Elly is also exceedingly vain on top of being as dumb as dirt and almost genetically incapable of seeing all the good things in her life. To be given a sort of sympathy prize from someone who wants other people to focus on what matters is not something that can occur to her while being thought of as being central to this woman's existence is.