The term EATS INTO can be solved by two crossword solutions: ERODES (6 letters) and ETCHES (6 letters). ERODES is a verb that means to gradually wear away or destroy something, usually by the action of wind, water, or other natural forces. ETCHES is a verb that means to cut or engrave a design into a hard surface, such as metal or stone. Both words refer to the process of wearing away or destroying something, which is what the term EATS INTO implies.