Plastic laminate or "Formica" is again becoming one of the more popular finishes for kitchen countertops mainly because of the myriad of patters and finishes that are now readily available. Unfortunately, although the cosmetic aspects of the product have significantly improved over time, you still can't place hot items (i.e., pots, pans, or coffee pots) upon the surface without experiencing cracking, blistering, or de-lamination. To many this is not a real disadvantage so long as hot pads are available and considering that plastic laminate remains one of the least expensive alternatives for new kitchen counters.
We are not familiar with any proven fix or technique, short of replacing the entire top, that will restore your top to its original condition. None the less we have come up against this problem on occasion and seen repairs successfully made using a maple butcher block patch. Using this technique, the damaged area is cut out and a piece of maple butcher block is installed in its place using a metal trim ring, similar to the one used to install sinks in this type of top. You actually end up with a bonus here. Not only do you get rid of that unsightly damaged area, but you create a nice cutting surface that, depending upon the configuration, can be quite an attractive addition to your kitchen.
If total replacement of the tops is not in order, (ok, not in budget) and this sounds like something you'd like to consider but aren't prepared to take on yourself, we suggest you contact a small repair contractor, countertop fabricator, or cabinet contractor. One of the three should be able to help you. And Mable, next holiday tell your loved ones to hold off on the dish towels and come through with some pot holders.