Now that you're looking at a checklist on an item page, here are some ways to interact with that checklist.
Not sure how to find the checklist on an item page? See View a checklist.
If two users try to modify a checklist at the same time, only the last user’s modifications are kept. In other words, if you don’t have the other user’s changes on your screen and you update the checklist, you’ll overwrite whatever was done by the other user.
Therefore, make it a habit to refresh the checklist before you edit it. This ensures you're editing the latest version.