Murray's lawyers tell TMZ, the woman -- who appeared to be in her 40s and of Eastern European descent -- visited Murray in jail Thursday, saying she flew in from Nevada just to see him.

Murray didn't recognize her and insisted there must be some mistake -- but she replied, "I've seen you before and you've probably seen me before. I'm the mother of Michael Jackson's kids."

FYI -- Debbie Rowe is the biological mother of MJ's two older children. The mother of the youngest child (Blanket) is reportedly a Hispanic woman in San Diego.

So needless to say, we're told Murray called the visitor an "impostor" ... then told her to scram, which she did.

Now, Murray's upset ... because a recent change in the L.A. County jail's visitor policy -- which lets visitors sign up online without verifying their identity -- has left him exposed to crazies from the outside world.

Under the new policy, prisoners don't even get notified of their visitor until they're sitting face-to-face with them in a tiny cell -- separated only by glass -- which is what happened to Murray.

Murray's attorney Valerie Wass tells TMZ, "I have serious concerns about the security. My client was horror-stricken by the fact that complete stranger could get in to see him."