Stressing he had not himself shared the image, Mr Monehen added: "Is it possible that someone could interpret that image about the state of Israel, not the Jewish people?"
Ms Drew's message of support appeared on Mr Monehen's Twitter feed on Wednesday after Labour reacted swiftly to the JC's report and removed him from the candidate list ahead of a planned hustings on Wednesday.
George Galloway was also among those to offer support - alongside activists who suggested "Israel" was behind the campaign to remove Mr Monehen.
One Labour MP contacted the JC on Thursday to express their "disgust" at Ms Drew's support for Mr Monehen.
"How on earth can a candidate selected to fight the election in Bournemouth East come to support someone who has clearly defended an appalling image," the MP added.
Ms Drew is an outspoken campaigner for the Palestinian cause, and said in her Tweet that Mr Monehen's own support for the same cause had "never included discrimination towards Jewish people."Â
Earlier this year, Labour suspended an activist in Liverpool Riverside after Dame Louise Ellman, the MP who resigned from the party last week, repeatedly complained about the circulation of the image.
