What you're describing is a sort of proxy that returns basic information from an external website. I don't think it's a weird question at all, and I know of a couple of attack scenarios.
Your design practially allows SSRF (Server-Side Request Forgery) by design. This doesn't have to be a big deal, but can have serious consequences. For example, if you run your application in AWS, one can call the AWS meta-data endpoint, which in some cases can grant an attacker temporary access keys to parts of your AWS environment.
SSRF can also be used to access your internal network, the server's loopback interface, and other endpoints that your server is whitelisted for. You've got to make sure to blacklist internal addresses (I would resolve the domain and parse the IP address to match certain ranges). And you've got to block the AWS meta-data endpoint when using AWS.
Are you using an XML parser to parse the external HTML? If so, make sure you're not vulnerable to XXE and secure your XML parser by not allowing External Entities.
Needless to say I hope you don't append your user's input into some system command, like
curl -s [URL], since that would allow for Command Injection. It's so stupid that I don't like to mention it, but I've seen people do it.
The rest depends on your application's architecture. Are you storing the data in a database? If so, make sure you're not vulnerable to SQL-Injection, etc. Good luck!