If you remove a member from a group (by unchecking him/her from the members of the group) and that group was registered to a program, the member will still have access to the program.
If you wish to remove the member's access to this program, you can remove him/her from the program's participants. To do this, you must edit the relevant program and uncheck the learner's name in the list of participants.
Important note: Removing members will mean losing the statistics they generated for that program. It will however still be possible to view these statistics via the users' profiles.