How to tell it is grease? Note the affected area. The height is reduced. Note the width of the devices on the affected areas. Note they are wider? The die fills the grease and prevents part/all of the strike. When the die is not totally full. They look like your coin wider. The device are tapered at the top and wider at the bottom. That allows the coin to not cling to the die. so they fall away from dies easier. Here are some simulations of how the grease can affect the dies:
Another even can reduce the height and widen the devices. That would be coin contact with a device. It will more or scrape off the devices leaving them altered. But when this happens the tops are not smooth like the grease fill event.