Tested in Firefox.
During installation: "* Access your data for all websites". If LT controls the text, change it to say what you mean. I don't understand "access you data for all websites". It seems as if I give LT permission to take my data for all websites that I visit (whatever that means).
Continue and don't ask again
Add an option: Continue and also ask next time
Enhancement: Let users move the message box.
Enhancement: Keep the message box on top of the web page.
The X to close the message box is not clear:
"Text checked remotely by languagetool.org" opens a new tab, but the tab is empty.
The icon 'Disable for this domain' is not always visible: