It revolves around the phrase "the greatest spectacle in racing," which was originally trademarked by former track owner Hulman and Company in 1986, and which has been used extensively in promotion ever since.
Early last year, the Liberty Media-run Las Vegas GP used the phrase "the greatest racing spectacle on the planet" on social media, and subsequently, Boles expressed his displeasure to F1.
At the time, he told the local newspaper the Indianapolis Star, which has been monitoring the ongoing dispute: "They couldn't have been more gracious, saying, 'Yeah, yeah, we've got it, no problem."
However, the American venue's frustrations were further ramped up when subsequently the words "the greatest spectacle in motorsports" were used by musician LL Cool J as part of his introduction of the drivers on the grid before the Miami GP.
After a further conversation between Indianapolis management and F1, the latter agreed to no longer use similar wording in any promotional activities.
While the earlier incidents were under the control of F1 and Liberty Media, Indianapolis was further riled this week by the use of the same phrase by their US broadcast partner ESPN, with "the greatest spectacle in motorsports" mentioned in a season preview trailer voice-over.
In a statement given to Autosport Boles said: "We are aware of the use of our mark in what appears to be a broadcast promotional spot.
"We will once again address it with the appropriate people and are prepared to take every measure possible to protect our brand's intellectual property.
"It continues to be disappointing that others can't create their own brand identity without infringing upon ours."
The ESPN incident came just a few days after a NASCAR social media post used "the greatest spectacle in racing," the exact words trademarked by Indianapolis, although it was quickly removed.
Boles has made it clear that the venue has to work hard to protect its trademarks, which are often used on unauthorised merchandise.
"You have to enforce it every single time," he told the Indianapolis Star.
"Sometimes people give us a hard time when we shut down a mom-and-pop company, but if you don't shut [them] down, and someone like F1 does this, then you have no standing to shut them down. But it's harder these days. You didn't use to have all these different mediums."
