Pipe the result of a cut command to curl

Leverage command substitution, $():

curl "$(grep ... | cut -d, -f 3)"

Here $() will be substituted by the STDOUT of the command inside $() i.e. grep ... | cut -d, -f 3, as this is done by the shell first so the curl command would be finally:

curl <the_url>

Another solution without substitution:

grep theName | cut -d, -f 3 | xargs curl > result.txt