How do I delete a calendar item from my day plan altogether without deleting it in Google Calendar?

You can hide suggested calendar items by clicking the icon to the right of the project category field. If your item is not recurring, it will simply disappear. If your item is recurring, you'll need to choose whether you'd like to hide just the one instance or all of them.

When there are hidden calendar items in your day plan, you'll see an eye icon between the last task in your plan and the Finalize Day button.

Click that icon anytime to see the items you have hidden in that day's plan. You can add any of those items to your day plan by clicking the [+] icon to the left of the item's task field. Re-hide hidden items by clicking the eye icon again.