I've always related grep to grab

"zu greifen" may best translate to "to grip", but "grip" has different mental connotations in English (it refers to mental stability, not intellectual insight).

The best dual purpose translation of "zu greifen"/"gripe" (German/Scandinavian) meaning "zu begreifen"/"begripe"/"understand" would be "to grasp", which covers both physically grabbing into something and also to understand it intellectually.

All these words stem back to the Proto-Indo-European gʰrebʰ, which more or less completes the circle back to "grep".