Hi. The way you would do this is to use our command api to set the "complete" property of a CheckListItem to true. You first need the uuid of the checklist item which you can get from the list that owns it. Once you have that you can post this data:
["set", "/UUID(...)/", "complete", true]
to this api end point:
/users/me/commands
For more details on modifying items see this documentation:
I hope this helps.
Regards,
Chuck