"Push Notes" are something that the receiver receives immediately depending on the "Delivery" option you have selected.
In case you select the "Now" option, the receiver receives the "Push Notes" immediately. However, if you select the "Later" option, you can delete the "Push Notes" before the scheduled time of delivery and make sure that the receiver never receives the "Push Notes". You can do this by simply clicking the "X" symbol. As soon as you click that button, a message will pop-up at the top of the screen asking to confirm your action and you just have to click the "OK" button to delete the "Push Notes".
In case you see the "✓" symbol, this means that the "Push Notes" has already been delivered to the intended receiver.