The council (as the employer) can direct that the clerk work in a specific way but if, as you say, the council don't want the poll anyway it is unlikely that they would even want to give specific direction to the employee in this regard.
Whilst it may seem (and it may even be) a petty attempt to minimise (quite literally) the publication of the notice, there is nothing to stop any interested party taking to social media to spread the word more broadly.
A member of public wouldn't have any recourse to try and encourage better publication or working practice by the clerk - other than by raising the question to the council.