How to grep the output of cURL?

curl writes the output to stderr, so redirect that and also suppress the progress:

curl -v --silent https://google.com/ 2>&1 | grep expire

The reason why curl writes the information to stderr is so you can do:
curl <url> | someprgram without that information clobbering the input of someprogram

It is possible to use --stderr - as parameter, to redirect the output from stderr (default) to stdout. With this option you also should use --silent to suppress the progress bar.

$ curl -v --silent https://google.com/ --stderr - | grep expire
*    expire date: 2015-09-01 00:00:00 GMT