Another year later, I was surprised this feature didn’t launch the app. I guess Monzo would need to write a screen with an Accept/Deny button but that doesn’t feel like an insurmountable task!
I had to put my Monzo details in manually on the web, which allows for data entry errors if this is a heavily-used feature.
Plus the first time I used it, it was trying to PUT https://internal-api.monzo.com/pay-anyone/claim-fps and got a 404 thus the button didn’t work. Started again and it worked though. 
Found this link for voting for this “feature”
Also this other thread which could probably be linked/merged