Protesters occupy a main road and walkways during a rally against a proposed extradition law in Hong Kong on June 12, 2019.

Beyond just the effects of this week, the mass political demonstration has raised long-term concerns about the future of doing business in the territory.

Meanwhile, Hong Kong's equity benchmark, the Heng Seng Index , slid 1.5% in early trade on Thursday, extending losses from Wednesday afternoon as tensions escalated.

For their part, major international banks including Standard Chartered, Bank of China and DBS said they had suspended branch services in the city's central business district area until further notice. For many financial firms based in the Central district, it was business as usual — but many offered staff the option of working from home.

Local government offices in the city's financial district have shut down for the rest of the week after several days of protest.

The mass political demonstration has already had an impact on business in the city.

Protests against a proposed change to Hong Kong's extradition policy continued on Thursday as several thousand protesters demonstrated in the streets — undeterred by the tear gas and rubber bullets police fired at them a day earlier.

The Hong Kong General Chamber of Commerce released a statement in March indicating its distress about the city government's proposal to allow extradition to several places — including mainland China — where it does not currently have obligations to send those accused of crimes.

While such a system may not sound like a problem for companies, many have expressed concern that it will undermine Hong Kong's rule of law, and subject those doing business in the city to Beijing's whims.

Those "new arrangements," according to the chamber, "will reduce the appeal of Hong Kong to international companies considering Hong Kong as a base for regional operations."

Such an overt opposition surprised some because the American Chamber of Commerce, and the local business community more generally, tends to avoid direct statements criticizing mainland China and Hong Kong's relationship.

When asked for comment on the latest developments in the city, the Chamber of Commerce said Thursday it has nothing to add beyond its March statement.

But not every business group is against the bill.

In a statement released on Thursday, The Hong Kong General Chamber of Commerce said it agrees with the underlying principle of the extradition bill. However, it added, the large-scale demonstrations and protests show that the community still has serious apprehensions.

"We sincerely urge the Government to continue to listen to stakeholders and engage in meaningful dialogue with the public," Aron Harilela, HKGCC chairman, said in the statement.

Still, it's significant that some businesses are speaking out against the extradition changes.

Joseph Cheng, co-founder of Power for Democracy, a pro-democracy political group based in Hong Kong, said the American Chamber of Commerce adopting "a public position against the Chinese authorities" is not only "rare," but also very "significant" for the local business community.

That sentiment was echoed by Ho-Fung Hung, a professor in political economy at Johns Hopkins University. Speaking with CNBC's "Street Signs" on Thursday, he said an amendment to the extradition policy could jeopardize not only the territory's reputation as a financial center but also its special economic status with Washington.

"What is practically worrying me is that Hong Kong always enjoyed a special trading status according to U.S. law, which is the U.S.- Hong Kong Policy Act, that separates Hong Kong from mainland China in many economic and diplomatic issues," he said.

For one, U.S. Speaker of the House Nancy Pelosi suggested that Hong Kong may, if the extradition changes are made official, no longer be "sufficiently autonomous" to justify a special trade arrangement between the territory and the United States.

What makes Hong Kong companies different from Chinese companies, he added, is that they have more access to U.S. and other countries' markets due to the special agreement.