The prank was organised after Muirfield yesterday announced the club will hold its second vote to admit female members in the space of two years.
Muirfield was accused of being “stuck in the dark ages” after the May 2016 vote which fell 10 short of admitting female members - a result that was condemned by SNP Leader Nicola Sturgeon and a number of other politicians.
The result meant to not allow female members resulted in the removal of the Scottish venue from the roster of clubs eligible to host The Open.
The bookmaker is offering odds on the outcome of the vote with the decision to not allow female members being the favourite outcome.
A spokesperson from Paddy Power said: “The decision last May to not admit female members was about as progressive as a Donald Trump policy, and unsurprisingly it’s driven a wedge between stuffy members and the outside world.
“While Muirfield members bury their heads in the sand this time round, we thought we’d prod the beast with our Jurassic sign.”