I recently updated a domain mapping for my domain but the TTL was several days
That'll teach you to have a long TTL for no good reason! =) 3600 seconds is the most that's reasonable in the vast majority of situations. I personally prefer 5 minutes even for domains that get hundreds of requests per second or more. Actually, especially if the record is pulled hundreds of times per second or more.
How can I send a message to the recursive resolver to tell it that its current entry is invalid and it should talk to the authoritative nameserver?
If you don't control the name server, you can't. If you do, then you'll need to search the documentation for the DNS server software to find out how to purge a specific record. Otherwise you're going to have to figure out . who to contact that controls the server. If it's an ISP, then just headbutt a claymore. Your demise will be less painful and messy.