The federal jury verdict that acquitted four Teamsters union members of attempting to extort the “Top Chef’’ television show also served as political relief for Mayor Martin J. Walsh – given City Hall’s connections to the case, according to legal and political analysts.

“If he doesn’t have this cloud hanging over his head by a conviction, it may just turn out to be a small victory,’’ said Peter N. Ubertaccio, a political science professor at Stonehill College who follows Boston politics. “It’s not an excuse for poor behavior, but it’s not extortion . . . and at the end of the day, it’s an acquittal.’’

The original September 2015 indictment of the Teamsters members — for crashing filming of the television show while demanding jobs — had become an early headache for Walsh, a longtime labor leader who was elected with heavy union support in 2013. During the trial this summer — months before Walsh stood for reelection — the Teamsters were accused of strong-arm tactics, bumping crew members, and slashing their car tires, though they contended they were only picketing.

Prosecutors had alleged that Walsh’s tourism chief, Kenneth Brissette, acted on behalf of the Teamsters and warned two Boston restaurants that the union would picket if they continued with plans to host filming of the show. The restaurants then cancelled their participation, forcing the show to relocate to the Steel & Rye restaurant in Milton, where the Teamsters aggressively picketed.

Several witnesses testified at the recent trial in federal court in Boston that Brissette had discussed withholding permits for the show unless producers hired the Teamsters as drivers.

At the time of the Teamsters indictment in 2015, Brissette had not been accused of any criminal wrongdoing, though an independent investigator for the city who reviewed Brissette’s involvement in the scandal questioned whether city officials should get involved in private union investigations. Walsh said he would revisit city policies.

On Tuesday, the mayor said he was relieved the case is over, for the sake of Boston.

“The city of Boston was not on trial here, though it seemed like it. This was an incident that happened in Milton,’’ the mayor said, adding he does not condone union rough-housing. “I’m glad the trial is behind us now, and so we can move on.’’

Walsh also defended Brissette’s alleged role in the case, saying he never withheld permits. The mayor pointed out that he was on an earlier episode of the show that filmed in Boston.

When asked whether the testimony under oath in the “Top Chef’’ trial contradicted Brissette’s denial, the mayor noted that the four defendants were ultimately acquitted, and he questioned whether “the answer is somewhat in the middle.’’

Since the original Teamsters indictment, Brissette and Timothy Sullivan, the city’s head of intergovernmental affairs, have been charged in a separate case with extortion, based on similar allegations that they withheld permits for the Boston Calling music festival until organizers hired union stagehands. Both have pleaded not guilty, and they are slated to go to trial in January.

Walsh referred questions on that case to the US attorney’s office in Boston, which is prosecuting. Sullivan and Brissette remain on paid leave.

Acting US Attorney William Weinreb said in a statement Tuesday that the jury’s verdict in the “Top Chef’’ case, while disappointing, would not dissuade prosecutors from pursuing extortion charges when appropriate.

Ubertaccio, the political science professor, said that the allegations in the Brissette and Sullivan case may differ from the “Top Chef’’ case, but he said that the acquittal of the Teamsters members could send a message that prosecutors have been overzealous in investigating unions, which could benefit Walsh.

“I think despite that they are different issues, they are all related politically,’’ he said. “And the acquittal here, I don’t know what bearing it has legally on the Brissette case [that is pending], but politically it adds fuel to the claims he’s being unfairly prosecuted.’’

Paul F. Kelly, a labor lawyer, said the “Top Chef’’ acquittal could force prosecutors to reexamine how they pursue extortion charges involving unions and those acting on their behalf. Kelly represented the AFL-CIO in a court motion to dismiss the charges in the “Top Chef’’ case, on the grounds that the charges criminalized lawful union activity.

“I suppose you could take away from it that pressuring non-union employers to put union people on the job is not [extortion], whether it’s done through City Hall or directly on the job site,’’ Kelly said. “You could at least be chastened to that extent.’’

The case against the Teamsters members was the second of its kind that federal prosecutors have filed in recent years. Three other Teamsters were convicted of similar allegations of extorting non-union employers. The federal appeals court in Boston is reviewing that case.

Valencia can be reached at milton.valencia@globe.com.