The term 'ANNOYS PERSISTENTLY' can be summarized by three crossword solutions: BADGERS (7 letters), GRATES (6 letters), and NAGSAT (6 letters). Badgering is a form of harassment or annoyance, usually involving persistent questioning or nagging. Grating is the act of making a harsh, unpleasant sound. Nagging is the act of constantly and persistently reminding someone to do something. All three words describe the same concept of annoying someone persistently.