From what it claims, it doesn't send any data, and it's stored locally, however, I don't see a reason to keep it anymore, nevertheless, it does look like a safety concern.
What is the name of the extension? I would like to dump the source code of of it to see if it sends data anywhere.
Link: https://chrome.google.com/webstore/detail/fea-keylogger/fgkghpghjcbfcflhoklkcincndlpobja?hl=en
I installed the extension on a Virtual Machine, found a few issues right off the bat.
The extension communicates with the internet, something that "Only saves data locally" shouldn't connect to the internet. They're is also another issue with the extension, it logs specifically logins, not just web pages visited and such. After further analysis, the data that it saves isn't even hashed, meaning that all of your logins are compromised if someone gets the data from your local storage of the extension.
My advice would be to uninstall the extension, reinstall chrome, then change all of your passwords.
On the other hand, do you know any kind of similar software that is safe to use?