It's usually hit or miss on a very simple mechanism, whether you can flush old hardened grease out or the new grease just finds a path past it.
I would get some of the (wrong) grease and confirm it dissolves in gasoline, take the tie rod end off, pop the boot off (if it can be done without damage which it may not) and agitate it in a tube of gasoline while wearing nitrile gloves to get ALL grease out, then shake out excess gas, let dry, re-grease.
However, if one of your tie rod ends is shot, odds are the other one has enough wear that I'd just replace it too, unless for some reason it is very expensive with no good aftermarket alternative.
I suppose that if you have no confidence you can get the wheel toe-in correct after removal for cleaning or replacement, this might be a reason to leave it in place, pop the tie rod end stud out of the knuckle, take the grease nipple off, liberally spray brake cleaner in, work the joint around to loosen the grease, then repeat spraying and working the joint a few more times, THEN re-grease. Once you get all the old grease out, you might find it is looser than you thought and end up replacing it anyway.
Last edited by Dave9; 07/06/19 12:48 PM.