Well yes, the best way is simply to remove the IPv6 in your DNS. If your service is not responding on IPv6 but you keep this IPv6 in your DNS, it’ll force every client on the internet to first try IPv6 and then fallback to IPv4, adding unnecessary network load and delay. That is why updown.io considers this configuration partially down.
Alternatively if you're really sure you want to keep this incorrect configuration and understand the consequences, I can disable the dual-stack check monitoring for you so updown will only check either IPv6 or IPv4 as long as one is working (like a browser). Let me know if you want that.
Another option can be to use an IPv4 in your URL directly (e.g. http://1.1.1.1/) but that will only work if you server accepts such requests (won't work if you have vhosts for example) and it won’t be able to validate you SSL certificate if any (because there is no hostname to compare it with).
And finally ideally you should work on making your services respond to IPv6 if possible 🙂