This is the 14899th most frequent German word.
reumütig
Remorseful; repentant.
Here, "reumütig" is used in its adjective form to describe the emotional state of the person, highlighting regret for a wrongdoing.
Nach seinem Fehler war er sehr reumütig und entschuldigte sich.
After his mistake, he was very remorseful and apologized.
In this sentence, "reumütig" modifies the verb "blickte" to describe the manner of her retrospective action, emphasizing sincere regret.
Sie blickte reumütig auf ihr Verhalten zurück und versprach Besserung.
She looked back remorsefully on her behavior and promised improvement.
"Reumütig" is directly describing the noun "Mann" as being filled with remorse, showing its attributive usage.