During the meeting coun Duncan tweeted: "Tory councillor Mary Mears appears to be wearing swastika motif on necklace at @BrigtonHoveCC meeting. What's that about? A #masonic thing?"
But when the tweet was brought to the attention of coun Mears she pointed out that it was a St Brigid's cross and said his green councillor colleague Phelim MacCafferty would be able to explain what it was.
Coun Duncan wrote the tweet during a debate about the March for England and Conservative coun Graham Cox described the tweet as offensive.
The Green councillor later tweeted: "Gosh it’s easy to wind Tory councillors up here!”
Speaking after the meeting coun Mears said she had found the tweet "very offensive".
Counc Duncan apologised for any offence that he caused.