When I cat a binary file, I get ‘PuTTYPuTTYPuTTY’ on my command line.

PuTTY

A.7.10 When I cat a binary file, I get ‘PuTTYPuTTYPuTTY’ on my command line.

Don't do that, then.

This is designed behaviour; when PuTTY receives the character Control-E from the remote server, it interprets it as a request to identify itself, and so it sends back the string ‘PuTTY’ as if that string had been entered at the keyboard. Control-E should only be sent by programs that are prepared to deal with the response. Writing a binary file to your terminal is likely to output many Control-E characters, and cause this behaviour. Don't do it. It's a bad plan.

To mitigate the effects, you could configure the answerback string to be empty (see section 4.3.7); but writing binary files to your terminal is likely to cause various other unpleasant behaviour, so this is only a small remedy.