Can repeated, petty complaints to HR be considered some form of harassment?

Q. A more senior employee was recently passed over for a promotion because a newer employee is clearly more qualified. Now that this person is their boss, the more senior employee has filed several petty complaints against her. Although we are aware that these complaints are completely invalid, we in HR have to take it seriously. But it is a shame for the new supervisor to have the complaints piling up in her file. Is this considered harassment?