You can redirect curl's output to a file with the -o filename option (or with > filename for shell redirection). But in the case of sites like this which output ansi-escape-formatted data that isn't very useful.
Also, after saving unknown data to a file it's common to look at it with less or perhaps xxd or strings or file ... all of which have had their own CVEs in recent years 🤦
Computer security is a fractal of bad news.