The Search field in monday searches in all columns. Since checklists are stored in a text column (the Data Column), you can search for checklist items.
Simply enter your checklist item in the Search field. The search will return all monday items with that checklist item.
It’s possible for monday items without the searched checklist item to be returned, if the searched text is found in another column. Remember, Search looks in all columns.
Search for unchecked checklist items
If you’re using Checklist for monday as a to-do list, it can be useful to search for checklist items that aren’t checked (i.e. they’re still to-do).
Enter "checked":false in the Search field. The search will return all monday items with unchecked checklist items.