Is checking the oil in a fridge as straight forward as a car

Yes, take it back. It is obvious that the mark was caused by a burn. The silver flashing tape was placed over it in an attempt to hide the damage.

I realize this is an old question, but for anyone else that comes across this:

First thing I would check is the house water pressure. Ice makers are typically operated by a timer and are designed with a specific water pressure and flow rate in mind. You can get a pressure measuring tool that screws on to a garden spigot from any of the big box stores. Make sure to check the pressure when all other valves are closed and the hot water heater has been running, since you may have a check valve in the line and experience high water pressure only after the hot water heater has been on.

As a backup option, I'd consider partially closing the valve to the ice maker line. You'll still have an initial surge of high water pressure, but the flow will be restricted. This may require some careful fine tuning to get just enough water to fill the tray without overflowing.