Using an Echo and the Alexa app with a captive portal can be hit and miss. The first step would be to run the wifi setup process and see if you get the hotel login. if not, there are a couple of ways people have made it work.

This post seems to work for a number of people,so follow those steps.

https://www.reddit.com/r/amazonecho/...ampus/du9b8sh/

Also, I've been pretty successful calling the wifi support line at the hotel and having them add a MAC address for me. If you give them the MAC address of the echo, it should connect without needing to log on, and that should eliminate any issues (once you go through the wifi setup process).