There are a couple of ways this might be possible. If you set up a default filter on a sheet to always load rows where complete box is unchecked, then, if you checked off a task or two and reloaded the sheet those tasks would not be visible the next time it loads. 

To do this: 

1. Create a new filter.
2. Title it and check the Share Filter checkbox
3. Set the criteria to the checkbox is unchecked
4. Then click okay
5. Save the sheet to save the shared filter. 
6. Click on SHARE
7. Scroll down and click edit next to the default view
8. Set the filter to new filter you saved
9. Save. 
10. Check off some boxes and save the sheet. 
11. Reload the sheet and the completed items will not be visible.

See attached screenshot. (Right-click on the image and view in tab. 

Glad I could be of assistance. Hope its working well for you.