How to remove the "Summarise" link from the top of the emails in Mail. I have Apple Intelligence turned off.

You cannot. It is part of the macOS Mail app user interface and cannot be turned off by the user. Only Apple can alter that.  

To have Apple consider your feedback, submit it here:

Feedback - macOS - Apple

As a workaround, you could consider an alternate (3rd party) email client. Or just ignore it.

Regarding turning off Apple Intelligence… Apple Intelligence launched with macOS 15 Sequoia (and iOS 18), and since then it has become progressively more integrated with macOS (and iOS). On macOS 26 Tahoe, there was option to turn off Apple Intelligence (though doing so did not remove the 12-14 GB of local storage taken up by Apple Intelligence features). 

On macOS Golden Gate, the toggle above has been removed, and Apple Intelligence is even more tightly integrated with macOS. Consequently, it is very difficult to turn off. Long-time forum member etresofthas written a helpful tip on how to Turn off Apple Intelligence in macOS 27. The title is somewhat misleading, Apple phrases it more accurately in their support article:

Turn off and restrict access to Apple Intelligence features on Mac

As Apple states, you can turn off and/or restrict access to some features of Apple Intelligence, but you cannot turn off Apple Intelligence altogether.

Apple Intelligence features can be restricted in a more comprehensive way by using a declarative configuration, but that requires device enrollment (i.e., management of the Mac with MDM) and that is beyond the typical processes with which most users are familiar. However, there is a script called Remove Mac AI that is available to execute those functions as a local Profile via a terminal command, if you are comfortable using it. At least one long-time member here has done so without issue. Use it at your own risk.

The button to summarize is not removable, but you should not be seeing your emails summarized.