Vindictively is the adverb of vindictive: it describes doing something out of a wish for revenge, in a way that goes too far. You put it next to a verb to say why and how an action was done. "She smiled vindictively" tells you the smile was not warm — it was the smile of someone watching an enemy fail. "He acted vindictively" says his actions were payback, and unfair payback at that. Because it carries a judgement, the writer is always taking a side when they use it: they are telling you this behaviour was petty and cruel. Watch where it sits in the sentence. It usually goes after the verb ("he replied vindictively"), or after the object if there is one ("he deleted her files vindictively"). Do not squeeze it between the verb and its object — not "he deleted vindictively her files". You will also meet it in a slightly formal register: courts, news reports, and novels use it more than everyday talk. In conversation people are more likely to say "out of spite" or "just to get back at her", which mean the same thing in plainer words.

報復性地、懷恨地、出於報復心地