For certain social media influencers, brand-sponsored trips are just part of the job. If they’re lucky, they may find themselves admiring the Instagrammably blue waters of the Greek islands, or perhaps the pink sunsets of Bali. But what about endless ocean views from the metal decks of an offshore oil rig?

“So, I need to, like, know by tonight, but I got invited on this brand trip,” a young woman told her boyfriend over the phone last week. “It’s with Exxon Mobil.”

A new prank on TikTok has prompted dozens of influencers to call their loved ones and tell them some version of the same story: that they have been invited on a brand trip to an oil rig off the coast of Texas, paid for by Exxon Mobil. Those on the receiving end of the call (who are not in on the joke) have had mixed reactions.

One father was generally supportive of the idea when his daughter proposed it on speakerphone. His reasoning? “People are not dying there.” Someone else responded to the proposition with confusion. “That’s definitely not her following,” she said of her influencer friend’s personal brand. “Her following is, like, girls that want limited-edition Chanel bags.”

Soph Mosca, 24, an influencer living in Los Angeles, wanted to see what sort of reaction she could generate from her father, Chuck. He told his daughter, accurately, “It’s a huge company to put on your résumé.”

“I was just seeing it all over my For You page,” Ms. Mosca said in an interview. “It was just from a bunch of just random people, but then also from some creator creators. And yeah, I just had to hop on.”

Zachary Weinberg, another content creator in Los Angeles, also wanted in on the fun. For the most part, Mr. Weinberg’s TikTok videos focus on reality TV, dissecting episodes of shows like “The Traitors” and “The Bachelor.” Over the weekend, however, he tried giving his followers something different.

“There was just something really funny about this trend,” said Mr. Weinberg, 26, “where I knew if I did it, I could get a really authentic reaction out of one of my parents.”

After a failed attempt to prank one of his friends who was already aware of the trend, he decided to call up his father. Mr. Weinberg’s father, Elliot, sounded perplexed by the offer. “First of all, you’ve never scuba dived before,” he said.

While he was more than happy to joke about it, Mr. Weinberg said that if such an opportunity actually did present itself, he would probably opt out.

“That’s not something I would want to do,” Mr. Weinberg said of the working holiday, as he imagined it. (His description involved “underwater welding.”) “But I would go on the trip and, like, take pictures of people doing it.”

Far-fetched as it might seem that Exxon Mobil, a $400 billion oil giant with operations in more than 60 countries, would call on social media influencers to help manage its image from the middle of the ocean, recent partnerships suggest that the idea isn’t entirely out of the question.

Last year, another industry leader, the ultrafast-fashion retailer Shein, sent a group of American influencers to one of its factories in China, spawning numerous glowing posts about the company. (“They weren’t even sweating,” one creator said of the factory workers she saw there.)

But the reaction to the creators’ content from the Shein trip was almost uniformly critical, with many pointing to accusations that the company works with suppliers that violate labor laws.

Exxon Mobil, whose representatives could not immediately be reached for an interview on Tuesday, is not, in fact, reaching out to social media influencers for partnership deals. Still, Ms. Mosca, who has over two million followers on TikTok, does have two personal requirements before working with any company.

“The biggest things for me are that I asked myself, Do I like this company? And then also, would my audience like this company?”