The purpose of putting cork in the reel seat, rather than having wood, is to reduce the weight of the rod. For this cork is great. It weighs next to nothing, really, when you think about the weight of the other hardware on the rod & the reel you'll mount.
That's why you see most of the cork reel seats as the cap & ring style seats like this one:
There are a couple of fixes for that. If the indentations from the reel feet aren't too bad, you can take them out with a bit of steam. Try holding your cork reel seat over a steaming tea kettle or other source of steam for a few minutes. Do NOT touch any of the metal hardware with your bare hands, as it will be hot, too & you could get burnt (don't ask me how I know that a burn from steam is worse than any other type of burn). As you steam the seat, you should start to see the cork expand a little & the indentations from the reel disappear.
If that doesn't work than you'll have to make a pad for your reel foot. A small strip of leather, about as wide as your reel foot, placed between the cork & the reel foot will help to hold your reel securely on the rod.
One note about the cork quality in the reel seat: some folks think that if the cork has any voids in it whatsoever, or if anything but the most perfect cork is used in the seat, than the seat will have a shorter life span. This is NOT true. It's okay if your cork has some voids, or "bark marks" in it. Cork is a natural product & no two rings are exactly alike. What really determines the integrity of the cork spacer is how well it was glued together. Most cork rings used in rod making are 1/2" in thickness. More thinner rings glued together will make for a slightly stronger spacer, but that is a very small point.
Another thing to know about cork reel seats is that, as a material, cork is more expensive than many of the hardwoods used in reel seats. That's right, you'll pay more for a cork reel seat than you will for a seat with a fancy figured wood.
These days it seems, from my perspective anyway, that cork reel seats are less popular than they used to be. They used to be found on many different sizes & weights of rods. It seems now that hardwoods are much more popular in reel seats. This, I think, is because the woods last longer & will take more abuse than cork. Also I think it's because there are so many options of woods to choose form that the reel seat spacer has become another component that can really customize your fly rod for you.