In short: never ever use an isolation transformer. Once you ground a part of the circuit you'll be creating a dangerous situation and the GFI won't protect you. Do yourself a favour and buy a proper differential probe. There are plenty of those (new!) on Ebay for reasonable prices.
An isolation transformer,by definition,does not have any part of its secondary winding connected to earth in the manner used for normal house power wiring.
If there is a connected "Earth" pin,it just connects to the Mains Earth & nothing else.
What were normally "Active" & "Neutral" inputs to the DUT power supply are now
both floating with respect to mains Earth.
Thus you are able to take
either of these to Mains Earth potential .
In other words,as they normally possess no potential to Mains Earth,they can take up whatever potential you like,so you can put the earth clip on either side.
OK,if you are seriously stupid,you could then get across the now earthed side & the other,but how much do we have to dumb things down?
Without an isolation transformer,get it wrong & you will blow the earth clip apart,& maybe damage your 'scope.
If the Mains Earth connection is made from the transformer input plug to the socket on its output,all it will do is take the common side of the output of the SMPS in the DUT to Mains Earth.
This output is isolated from the "mains" side of the SMPS by the inbuilt galvanic isolation of the supply.
After all,this is the main reason why we use SMPS in the first place!
If we didn't care about isolation,we could use the old AC/DC type circuits used in many post WW2 US radios.
Why they went to them is beyond me--pre WW2 US radios used power transformers.