The growing list of corporations severing ties to the Russian economy doesn't include Hyatt Hotels so far. Whether that changes in the days and weeks ahead will make another high-profile statement about the reputational risk of associating even remotely with the country's invasion of Ukraine.

Chicago-based Hyatt and its fellow major U.S. hotel chains have all been relatively quiet in recent days, while other well-known brands, including Visa, Mastercard, McDonald's, Starbucks and Apple, among others, have taken meaningful steps to at least temporarily shut down their business in Russia.

Hyatt posted on its website a humanitarian-focused statement on the situation late last week, noting the company is "heartbroken over the devastation unfolding in Ukraine and the mounting tragedies resulting from military actions, loss of life and the dislocation of hundreds of thousands of people. Our immediate focus is on the safety and well-being of our colleagues and guests in both Ukraine and neighboring countries who face these unconscionable challenges."

Related: How other brands are responding to the war

Responding to questions from Crain's this week about whether the company would continue to have a presence in Russia, a Hyatt spokesperson did not address the matter, instead reiterating the sentiment of the initial statement and confirming its relatively small footprint in the country: Hyatt operates—and does not own—five hotels in Russia, most notably, the Ararat Park Hyatt luxury hotel in Moscow.

But with every well-known American brand name that distances itself from Russia, the pressure mounts on Hyatt and its competitors to weigh the implications of following suit and cutting off business there against the backlash they could face if they don't.

It's a tricky calculation for Hyatt, says Scott Antel, a hospitality industry-focused attorney who lived in Russia for 22 years until 2015 and continues to consult with Russian hotel investors in the country. On one hand, no hotel company wants the optics of being affiliated with the aggressor in an unprovoked war, the same reason other major brands have shuttered Russian operations—even at the expense of big revenue lines. Hyatt could step away while only sacrificing the fees it receives from hotel owners, at least in the near term.

But removing a name and management service from a hotel also impacts hundreds of employees Hyatt has helped train that could then be out of work. They and future guests might harbor ill will toward the brand, which could make it difficult for Hyatt to resume business in the country.

"People remember these things. It's just not good," said Antel, who now lives in Dubai and is a member of the International Society of Hospitality Consultants. "Customer goodwill takes a long time to rebuild."

It's unclear who owns Hyatt's hotels in Russia, though Antel said the vast majority of hotels in the country are owned by various Russian investors and entities. If any of the owners are hit with sanctions from the U.S., Hyatt would abruptly pull out of the country to avoid penalties at home, he said.

For now, the Hyatt (backed by the Pritzker family) and its competitors are downplaying the impact of the Russian invasion on their business.

Speaking Tuesday at the Raymond James Institutional Investors Conference in Orlando, Hyatt Chief Financial Officer Joan Bottarini said the company is watching the Russia-Ukraine situation "extremely closely" but "we haven't seen any material impacts."

Marriott International CEO Tony Capuano said yesterday during the JPMorgan Gaming, Lodging, Restaurant & Leisure Management Access Forum in Las Vegas that the company has 28 managed and franchised hotels in Russia, which collectively represent less than 1% of the revenue it gets from fees. Russian travelers, he said, also account for less than 1% of all nightly hotel room bookings around the world.

"We are very focused on the safety of our associates and the safety of our guests in those markets. But from a materiality perspective in terms of the company's financial performance, (it's) not particularly significant," Capuano said of Russia.

As for whether the invasion will impact hotel business in Europe at large, Capuano said it's too soon to say. "Recovery around the world has largely been driven by traveler confidence. And depending on how the situation evolves in Ukraine, could that have an impact on traveler confidence to Europe? Of course."

Shares of Hyatt closed Tuesday at just under $85 apiece, roughly even with the company's stock price a year ago, but down 11% year to date.