When Jesus says that Tyre and Sidon would have repented in sackcloth and ashes, he invokes a familiar biblical picture of repentance made visible. Sackcloth was rough clothing, while ashes could be placed on the body or associated with mourning and abasement.
The image communicates grief and repentance in a form that others could see.
Across the biblical world, sackcloth and ashes appear in contexts of mourning, disaster, penitence, and self-humiliation. The actions externalize an inward condition and can become communal as well as individual signs.
Jesus' wording draws upon that established symbolic vocabulary. He is not prescribing a magical ritual; he is describing unmistakable, demonstrative repentance.
The background strengthens Jesus' comparison. Tyre and Sidon are pictured not as experiencing a vague change of mind but as responding with the most recognizable signs of penitence.
That makes the rebuke of towns that witnessed Jesus' mighty works more severe: greater exposure to revelation has not produced the response that even notorious outsiders are said to have made under lesser circumstances.