The most obvious target is Tencent's WeChat, which was the only product that Mr Pompeo called out by name in addition to TikTok.
WeChat is sometimes described as being a social network, but it's really so much more - offering ways to make payments, run additional mini-programs, find dates and get the news, in addition to messaging and other social activities.
It's perhaps best thought of as being a kind of secondary operating system that sits on top of iOS or Android.
Meanwhile, a recent study by security researchers at Canada's Citizen Lab detailed how documents and images transmitted among non-China registered users were being screened for content that the Chinese authorities would consider to be politically sensitive. It did not find that any were being blocked, but rather suggested the collected data was being used to refine censorship efforts within China itself.
Tencent has previously said all content shared among international WeChat users stays private.
India might give a hint as to which other Chinese apps could be barred.
The South Asian country recently banned 59 China-linked apps on the grounds they threatened its "sovereignty and security". TikTok and WeChat were on the list, and other big names included:
Baidu Maps and Baidu Translate - rivals to Google's products from China's leading search provider
Weibo - the Twitter-like micro-blogging service
Clash of Kings and Mobile Legends Bang Bang - two video games
CamScanner - a document-scanning product
QQMail - an email and file-transfer service
The BBC contacted several apps affected for comment, but did not receive a response.
But one expert suggested that a desire to help home-grown software developers, rather than "genuine security concerns", might have been a factor in taking the decision.
“What they’re definitely trying to signal is that India has had enough of China and wants to de-link itself,” commented Gareth Price, a senior research fellow at London-based think tank, Chatham House.
AliExpress, a shopping app from the Chinese online retail giant Alibaba
Video games from NetEase, which publishes several Marvel super-heroes titles among others
Tencent Games titles, which include Player Unknown Battlegrounds (PUBG) Mobile
Various Mi-branded apps from the mobile phone maker Xiaomi
The Indian press has suggested Finland's Supercell - developer of the Clash of Clans video game - might also be banned in India, on the basis that Tencent has a large stake in the business.
Were the US to follow that line of attack, League of Legends' publisher Riot Games, and Fortnite maker Epic Games, might also have reason to worry.
Mr Pompeo has also suggested that software which collects facial recognition patterns are a concern.
Although he did not mention any product by name, there are many Chinese companies that make such products.
The social network Kwai and beauty app YouCam Makeup both use facial recognition algorithms, and are among the Chinese apps banned by India.
It should be noted that US restrictions on Chinese firms are not entirely new.
In the past year or so, the Trump administration has added dozens of Chinese companies to economic blacklists, which restrict the firms in question from buying US technology without government approval.
Among those recently added are:
Qihoo 360, a cyber-security firm
NetPosa Technologies, which makes video recording devices
CloudMinds, a provider of internet-based tools to control robots
iFlyTek, a provider of voice-recognition services
Megvii and Sensetime, two facial-recognition tool providers
China responded by saying it was firmly opposed to the move.
Zoom is a further service that might have concerns.
The video chat service was founded by China-born entrepreneur Eric Yuan. It has faced criticism for having "mistakenly" routed some calls via China-based computer servers in the past, as well as having closed accounts that had hosted events critical of the Chinese government, but been based elsewhere.
The company has just announced it will stop offering its service directly to China-based users, and will instead provide it via local partners.
“We informed our customers that this will take effect on 23 August," it said in a statement.
The timing may be a coincidence, but the move demonstrates that tech companies may be wary of giving the US any reason to question where their loyalties lie going forward.