Complaint. Grinding an axe suggests preparation for a bloody confrontation, but in this phrase it implies only an argument to be made. Also a grinding axe makes a shrill sound and is a metaphor for irritation, especially if one has a long-time, lingering animosity. Have a nit to pick.
“She was so unfriendly to me. I didn’t know she had an axe to grind until I realized my dad had fired her.”