The petrol giant has finished installing its long-awaited Southampton to London pipeline.
But the works left parts of Fordbridge Park decimated and remedial works have been taking place.
But the council says rumours it has approved the work to rectify the damage done are false.
Councillors say they will not accept completion until the park is returned to a fit state for residents to use and enjoy.
Re-seeding is currently taking place, and a tree plan is in progress to plant 18 semi-mature trees.
Esso says its desired timeline for completion has been impacted by inclement weather and the need to allow seedlings to become established.
The spokesperson also says it anticipates the work will be completed to the highest standards.