How to better isolate a floor with carpet

You can make the floor water resistant by varnishing it. Two or three coats should protect it from most damage, especially if you lift the affected tiles straight away. Most damage is done by the prolonged contact of the water with the floor. Are you expecting a lot of spillage?

This does mean that you might want to consider not sticking the tiles down or only using a very light adhesive. If the tiles are well fitted and cover all of the floor area there shouldn't be any lateral movement in the tiles themselves.

Using a household iron works, with caveats.

First: several sheets of paper towel between the iron and the carpet. These are here primarily to protect your iron (and your shirts!). I was hoping that it might also might be something that the plastic preferred to stick to, but that didn't happen.

Second: no steam, and set the heat on wool (about 1/2). I slowly worked my way up the heat dial: the synthetics settings weren't hot enough (as expected), the cotton setting (3/4) wasn't appreciably better, and the linen setting (full) made the plastic adhere more tightly to the carpet (fortunately, I tried this near the end, to get the last bits out, and it actually had the benefit of making them disappear).

The process: put the paper towels over the spot, then let the iron sit for 20-30 seconds. This will soften the plastic, such that it can be removed either by pinching between your fingers or using tweezers. Fingers are preferred, as tweezers tend to tear out small pieces. In retrospect, a dull knife (such as a table knife) would have been a good tool: it would go on bottom, pulling the plastic away, with a finger on top to apply pressure.