The chatbot, which is accessed through Musk's social media platform X, has in the past few weeks been granting a wave of what researchers say are malicious user requests to modify images, including putting women in bikinis or in sexually explicit positions.
Researchers have warned that in a few cases, some images appeared to depict children.
Governments around the world have condemned the platform and opened investigations into the platform.
On Friday, Grok was responding to image altering requests with the message: "Image generation and editing are currently limited to paying subscribers. You can subscribe to unlock these features."
While subscriber numbers for Grok are not publicly available, there was a noticeable decline in the number of explicit deepfakes that Grok is generating compared with days earlier.
The European Union has slammed Grok for "illegal" and "appalling" behaviour, while officials in France, India, Malaysia and a Brazilian lawmaker have called for investigations.
On Thursday, Britain's Prime Minister Keir Starmer threatened unspecified action against X.
"This is disgraceful. It's disgusting. And it's not to be tolerated," Starmer said on Greatest Hits radio.
"X has got to get a grip of this."
He said media regulator Ofcom "has our full support to take action" and that "all options" are on the table.
"It's disgusting. X need to get their act together and get this material down. We will take action on this because it's simply not tolerable."
Ofcom and Britain's privacy regulator both said this week they had contacted X and Musk's artificial intelligence company xAI for information on measures they had taken to comply with British regulations.
Grok is free to use for X users, who can ask it questions on the social media platform.
They can either tag it in posts they've directly created or in replies to posts from other users.
Grok launched in 2023. Last summer the company added an image generator feature, Grok Imagine, that included a so-called "spicy mode" that can generate adult content.
The problem is amplified both because Musk pitches his chatbot as an edgier alternative to rivals with more safeguards, and because Grok's images are publicly visible, and can therefore be easily spread.
