North East Lincolnshire Council said workers had found a pair of gloves and an empty bottle, which they believe contained oil.
The authority has installed absorbent booms in the lake to soak up any remaining oil and said it would work with the Environment Agency to understand the longer-term impact.
Council officials also issued a plea to people to respect the parkland and be respectful of the area’s wildlife.
Commenting on the oil spill, Wolds ward councillor Henry Hudson said: “This is frankly unacceptable in every sense of the word.
“Not only is this disrespecting the beautiful open spaces that our borough offers, but it’s also putting the animals there in danger.”
Park users have expressed their anger over the impact it could have on the nesting bird population.
Jean Johnson, who regularly visits and feeds the swans, said: “I think it’s disgusting, how could anybody do that?”