Do you need to use anti-virus software on a Mac?

Probably not.

I’ve just loaded Malwarebytes on our iMac and MacBook Pro computers – provided by our bank – and only found one piece of tracker code, on one machine, which was very old and most probably not active. I deleted it.

Macs have a very good history of not being hacked, and when they are they close the problem down very quickly. This is a benefit of Apple owning both the hardware and software and being able to control which of the latter is installed on MacOS.