I think it is a cross between Pearl which is also a derivative of Margaret and Meggie.
I think that Margater is the greek version of Peral or something like that.
It's weird how these things come about isn't it?
I think that it was really to distinguish people from each other back in the days when we used a smaller variety of names and every 2nd girl was either Margaret or Elizabeth, so we then had all these other names to tell them apart e.g Meg, Meggie, greta, rita, peggy, pearl, Maggie ,Margie etc.