As per the link you would have to set up the Canary domain. On pihole you can add custom domain names and that should be enough.
Reading the documentation again you should even just be able to blacklist the domain and it'll make Firefox use local DNS in the network.
Not that unusual depending on the software. A lot of them honour the TTL literally.
One enterprise software I know that does it is VMware vcenter. I'm sure there's plenty of consumer software that retries excessively.