You're trying to delete it the way I showed you, with one minor exception. Your section is named channel.nick but you're using $+($chan.$nick) which is trying to access a no-such-identifier. To avoid this kind of mis-steak, go into the alt+R editor, and on the 'options' menu of that window, there's an option "identifier warning". Without that being checked, no-such-identifier resolves to be $null, but if you have a checkmark for that option, you'll instead get an error which halts the script.
What you should be using there instead is having the items inside $+(*) being separated by commas, similar to one of your commented-out lines, depending on whether you want to delete the item for $2 or for $nick:
If you want to delete the item for $2 but then fallback to deleting the time for that nick when $2 is not present, you can do like:
$+($chan,.,$iif($2,$2,$nick))
