Trademark rights to "Tavern on the Green"

Dinersjournal noted: The Tavern on the Green Food Truck Terrace, at 67th Street and Central Park West, opens for the first time this season on Saturday at 11 .m. and on Sunday [April 17] from 2 p.m. to 4 p.m. there will be free food and live music. The Ladle of Love, Pera Turkish Tacos, Rickshaw Dumplings and Van Leeuwen Ice Cream trucks will each serve one free dish per person. After this weekend, the food trucks will be open seven days a week from 11 a.m. until dusk.

IPBiz notes the "free food" for Saturday, April 16 was delayed because of anticipated rain.

Meanwhile, at the trademark ranch, a Bloomberg story noted that the most valuable asset of the former "Tavern on the Green" involved the trademark:

Lawyers for Tavern on the Green LP, which filed for bankruptcy in September 2009, and its creditors have said in court that the rights to the Tavern name were the most valuable asset the company possessed, estimated at $19 million.

In March 2010, U.S. District Judge Miriam Goldman Cedarbaum ruled that New York held the rights to the trade name, saying the city had maintained a restaurant under that name since 1934. The trustee appealed that ruling in May.

Query: does use of --Tavern on the Green Food Truck Terrace -- tarnish the rights to "Tavern on the Green"?