In 2 Timothy 2:25, metanoia, translated "repentance," is clearly used to signify, not just a change of mental state or an emotional response, but also the change in behavior that results from that response:
24 The Lord’s servant must not quarrel, but be gentle towards all, able to teach, patient, 25 in gentleness correcting those who oppose him: perhaps God may give them repentance(metanoian) leading to a full knowledge of the truth, 26 and they may recover themselves out of the devil’s snare, having been taken captive by him to his will.
2 Timothy 2:24-26 (WEB) (parenthetical added).
In the broader context, Paul instructs Timothy, among other things, to remind and charge his flock not to "argue about words, to no profit, to the subverting of those who hear" (2 Tim. 2:14). He then instructs Timothy personally to exercise diligence in study to keep his message pure (v. 15), to avoid empty chatter (v. 16), and to "flee from youthful lusts, but pursue righteousness, love and peace with those who call on the Lord out of a pure heart" (v.22).
Paul then moves on to discuss how Timothy is to behave toward those who set themselves in opposition against him. First of all, and contrary to most modern Christian practice, he is to avoid arguing with them! He is, Paul says "to refuse foolish and ignorant questionings, knowing that they generate strife" (v. 23); indeed, Paul says that, as the Lord's servant, he must not quarrel. Instead, Timothy is to respond to his opponents by continuing to patiently teach the truth, gently correcting his opponents. It is possible, Paul implies, that by continuing to teach the truth and treating his opponents gently, God will give even his opponents repentance leading to the knowledge of the truth. For those who are interested in such things, the Greek construction of this sentence-mēpote followed by an aorist subjunctive verb--implies that Timothy is not to expect that his opponents will repent. It is unlikely, but God may grant them repentance, and, because of this possibility, Timothy is to continue to be gentle with them and patiently teach them the truth, if they will hear him.
And what will be the result if God grants them repentance? First of all, they will be brought to the knowledge of the truth--the same truth Timothy is preaching--and, therefore, stop opposing Timothy. This is one change in behavior that will result from their repentance. But even more, they will recover themselves out of the devil's trap, and no longer be captive to do the devil's will. So their repentance will cause them to stop doing the devil's will.