So I put the new tensioner pulley on. The old one could be wobbled a bit and same with the new one, though it does not wobble while running, only if forced by hand. Bolt is tight too. Guess that is just the way it is. Strange though. Both pulleys are Dayco.
BTW, the old pulley probably would have been fine for a long time. Yes it clicked but the bearing was nice and tight. Only thing, when I put them on my finger and gave them a spin the old one spun freely but the new one only went around about one turn. That might suggest the bearings being loose in the old one.
Anyway, just as well to have the new one on there now and I only paid $21, where other places were $26 and $30. At any rate, old pulley or new, the chirp noise was gone with the new belt.