Since you are not related to your 3rd cousin's grandmother, who is her father's mother, whereas you are related only on her mother's side, you are not related in any way whatsoever to this grandmother's nephew's granddaugther. For instance.

But, in this case, since you present it as a "mind bender" - I will assume that *you* are your 3rd cousin's grandmother's nephew's grandaughter. Unless you have a sister. Then it could be her as well. So, you are either related as in identical to this person (in which case there is no name for the relationship) or you are her sister.

Meaning to say, there are several ways you could be related - or even not related at all - to your 3rd cousin's grandmother's nephew's grandaughter. But, I think she is you.