To modify a Course Participation you'll need to bring up the editor pop up.  This can be done from one of two locations:

1.  From the home page >> Courses area, click on a card for a given Course to load it into the right side panel.  There , in that side panel, click on the Participants tab, and then hover over the participant and click the edit icon that appears:

2.  From the Courses section of a Client or Group Page.  There, hover over the card of the course and click the edit icon that appears in the bottom right corner of the card:

In the pop up that appears, you'll see the various ways in which you can make changes to the in-progress participation:

These controls are by-and-large self explanatory, but do pay particular attention to the options concerning what to do with items when rewinding, fast forwarding, and stopping!  It's easy to make a bit of a mess if you get those wrong for what you intend, but by the same token such messages are generally easy to undo: just pay attention to the options.

If you pause the participation, simply revisit this pop up to manually un-pause, or change the scheduled resume date.

Customizing a course

This has the effect of removing the client from the Course entirely, including any records of their having been in it. You can choose whether the client keeps the Course items that have already been issued, or to delete them.  Being able to delete any course items from it is a great way to reset things, OR delete a lot that you didn't mean to, so be sure to get that option right!