signal - Using an earthed function generator with an earthed oscilloscope and ground loops

I have a function generator and I noticed that its DC GND is internally wired to its earth pin.

Similarly I have an oscilloscope and I noticed that its DC GND is also internally wired to its earth pin.

So now If I use this function generator with this oscilloscope(with 3-prong power cords) wouldn't there be a ground loop?

If so, should I use 2-prong power cable for one of the instrument to eliminate it as a solution?

EDIT: An illustration for the question:

On the left side the box represents the function generator, on the right side the box represents the oscilloscope.

Circles represent the BNC connectors.

Number 1 and 3 are analog grounds of the function generator and the scope.

Number 2 is the GND shield of the coax cable, where the coax cable is connected from function generator to the scope (i.e. function generator and scope GND are connected)

Number 4 is the earth wire

L, N, E are the line, neutral and earth pin of the 3-prong power cable.