Grand Cherokee WJ Limited slip diffs, and un-even tire sizes

[pcn1]

I'm getting a bit of a moan/groan from what sounds like the rear diff (or could be the transfer case, hard to tell) when making a right or left turn. (but not each time I turn funny enough) No noise at all when driving straight line.

So plan is to drop diff cover, clean out and inspect then fresh oil and FM additive. I've done this before so no bother.

However, I have noticed the Jeep has 2 new tire's up front (dealer fitted to get the MOT) and 2 half worn tires at back. But 1 back tire has say 5mm tread and the other has 5.7mm.

Is this discrepancy in tread depth front to back and rear side to side, enough to make the diff or transfer clutches kick in when I'm turning ???

Cheers

[MustangGT]

Should not cause a problem. Moaning can be the steering pump as the fluid is under pressure? Had that before on a few cars.
Never had any noises from any of our 4 Grand Cherokees (2004 - 2006).