the term comes from “hand-eye coordination”, which has nothing to do with robotics because animals with eyes aren’t classed as robots.
the “in” is irrelevant. it is “hand-eye calibration”. the pose between hand and eye (cam/gripper) is assumed to be rigid/fixed.
that is likely a typo or mistranslation.
I’m not seeing a verb but I’ll assume you meant to use “[does X] mean […]”