My first suggestion on the Grill Pan Tips page is to lower the heat while you are using your grill pan. To impress the importance of not overheating I have done a cut and paste from the user instructions of three grill pan manufacturers; Lodge, Les Creuest and Greenpan. While the first two companies are familiar to many people the third, Greepan is not. Greenpan is the maker of grill pans for the Martha Stewart and Todd English line of products.

• Use only low to medium heat settings for all pre-heating and cooking. The efficiency of the material is such that searing temperatures are achieved on medium settings within a few minutes. Heating the surface a little more slowly will ensure a thoroughly and evenly heated surface. (Les Creuest user instructions)

• Before cooking, apply vegetable oil to the cooking surface of your pan and pre-heat the pan slowly (always start on low heat, increasing the temperature slowly). (Lodge user instructions)

• Use only MEDIUM and LOW heat settings. DO NOT pre-heat on high heat settings. MEDIUM and LOW heats will provide the best results for the majority of cooking, including frying and searing. Allow the cookware to preheat gradually and thoroughly, as this will give the most even and efficient cooking results. Once the cookware is hot, almost all cooking can be continued on lower settings. (Greenpan user instructions)

• DO NOT pre-heat the grill on a high heat and then reduce to medium or low for cooking. Cast iron is a very efficient material and retains heat well. If over-heated it will retain that heat for a long time and this method of use may contribute to poor cooking results and the food sticking to the surface of the grill. (Les Creuest user instructions)

• At no time should the grill’s surface be smoking hot. This very high temperature is far from ideal for good grilling and may result in the outside of the food being over-browned and over-cooked before the center is cooked correctly or to your taste. If the surface is smoking, lower the heat immediately or, carefully remove the grill from the heat source to cool down before proceeding. (Les Creuest user instructions)

• Cast iron retains heat so well that if your cookware is overheated, it will contribute to poor cooking results. At these high temperatures, fats will burn extremely fast, damaging the surface of the coating permanently, leading to loss of the non-stick properties and discoloration of the cooking surface. (Greenpan user instructions)
The last comment by Greenpan refers to permanent damage to the non-stick polymer (Thermalon) that coats their grill pan and not to the enamel itself.

Seriously, turn the heat down a little.