There are two places where a member can be Checked Out of a mission.
Check In/Out Screen
When a member is currently checked into a mission and you visit the Check In/Out screen, they can be Checked Out in the upper right portion of the screen. The time and date can be adjusted from the currently displayed time, as long as the edited time is in the past. You may not check someone out at a future time. You may also not edit the check out time to be before the check in time. Either case will cause the member to be checked out at the current time.
This is the screen that shows the status of all the members that have been checked into a mission. When a member is ready to be checked out, you can use the drag and drop feature to grab the member from the Available Personnel column and drop them into the Checked Out box. Note that the current date and time will be used, unless you check the box next to the When Changed area to modify the Check Out date/time.