The theme park's owners said Swift's Evermore release had caused confusion about whether the two were linked.
The Utah venue said there was a "dramatic departure from typical levels" of traffic on its website in the week after the album's release.
Swift's lawyers responded that "there is no basis" for the claim.
They wrote in a letter filed in court: "Moreover, your client has suffered no damages whatsoever and, in fact, has openly stated that Ms Swift's album release creates a 'marketing opportunity' for your client's troubled theme park."
But the theme park owners, who are seeking millions of dollars in damages, have said the trademark for the name belongs to them, and that Swift violated it when she started selling album-related merchandise.
In the case, filed in a US District Court in Utah, the owners said they had spent millions of dollars on the attraction, which opened in 2018.
In December, the owners wrote to Swift's legal team to say they were "open to discussing reasonable terms for your discontinuation" of the trademark.
Evermore, which was released on 10 December, was Swift's second surprise album of 2020 and was described as a "sister album" to Folklore, which came out in July.
Both albums were critical and commercial successes, topping charts around the world, including in the UK and the US.