The letters were reinstated on Monday after the council told them they didn’t have permission to take them off a listed building.
The owner of the building, Danish retail clothing billionaire Anders Povlsen, had also expressed surprise and frustration at the move claiming that despite the store closing he had expected the famous sign to remain.
In April, Anders Krogh Vogdrup – the director of Povlsen’s group AAA United – said: "We are very surprised seeing the signage being taken down. We are convinced that the signage is part of the listed building.
“We have not discussed any such step with Sports Direct, and certainly not given any authorisation to do so. We will look in to this matter, contacting Sports Direct.
Frasers Group and boss Mike Ashley have now issued a statement claiming that they had made attempts to contact Edinburgh Council about the removal and had not heard back.
They also claimed that the landlord and council put more effort into protecting the sign that was put in to protecting the jobs of those who worked in the historic department store.
The statement said: "As has been reported, we have replaced the Jenners signage.
"We tried on numerous occasions to contact the council both prior to and after the removal of the Jenners sign, to no avail.
"Despite previously informing the landlord that we would reinstate the signage and ignoring the fact that Frasers Group owns the intellectual property rights to the Jenners name, the landlord also felt it necessary to waste public time and money in the issuance of court proceedings against us.
"Above all else, we regret that the landlord and the council weren't so proactive in protecting over 200 jobs when we were attempting to remain in occupation of the store at a huge cost to our own business and have instead spent all their time and effort, during what are incredibly difficult times, on the protection of a sign."
Frasers Group is owned by Sports Direct businessman Mike Ashley who took over Jenners in 2005.
A spokesperson for the city council said: "This is a category A-listed building and as such the council is required to have special regard to the desirability of preserving the building, its setting or any features of special architectural or historic interest that it possesses.
"For this reason, we served a listed building enforcement notice requiring the lettering to be reinstated.
"We did not receive any contact via the details included on the listed building enforcement notice after its issue, and are not aware of any contact prior to this."