Final answer:
Rumors about Clare Kendry involved her being seen with another woman, at a fashionable hotel, and with two men, which created gossip and affected her social relationships.
Step-by-step explanation:
The rumor about Clare Kendry involved her being seen with another woman and with two men. She had various encounters and relationships that stirred gossip within her social circle. One significant incident involved Clare being seen at a fashionable hotel with the son of the president of a great trust company. Another separate rumor hinted at her being seen at a station with the same man looking very mournful indeed. She was also rumored to have disappeared with another man after a picnic supper, which caused significant distress to her suitor, Dexter. Clare's actions and the associated rumors highlight the complexities and dynamics of social relationships and reputations during that era.