Here's what I've read:

In 168 BC the Rhodians had sought to mediate between Rome and Macedon. Rhodes indeed had a longstanding tradition of such diplomacy in settling quarrels between Greek states.

However, the news of the victory at Pydna reached Rome in advance of the Rhodian diplomats. As a consequence their intervention right after Rome’s victory appeared to the Romans as an attempt to protect Perseus, once he had been defeated.

The senate also still remembered the arrogant lecture it had received by the Rhodians, when Roman power in Greece had seemed to be on the wane.
For Rhodes it spelled disaster. One praetor even suggested war. But Cato the Elder counseled against it, realizing that no real malice had been intended with the bid to mediate.

This was however not accomplished without the utter humiliation of the Rhodian envoys who prostrated themselves before the senators, pleading tearfully for their city not to be destroyed.

Rhodes was to lose her territories in Caria and Lycia which had been granted her after the War against Antiochus. Furthermore she was to suffer a terrible blow to its trade with the punitive creation of the famous free port on the island of Delos.

But by 165/164 BC Rhodes was at last recognized as an ally of Rome again.