Step-by-step Solution:

\[ \textbf{Given:}\ \text{"John's mother's father's granddaughter is Maria."} \] \[ \begin{aligned} &\text{Let } M=\text{John's mother},\quad GF=\text{John's mother's father (maternal grandfather).}\\ &\text{A ``granddaughter of }GF\text{'' is any female child of }GF\text{'s children.} \end{aligned} \] \[ \text{One obvious female grandchild of }GF\text{ is }M\text{'s daughter.} \] \[ \text{M's daughter is John's sister (a female child of John's mother).} \] \[ \therefore\ \boxed{\text{Maria is John's sister.}} \]