There could be a relationship between the MINK and MINKE families, such as the case of my grandfather after arriving here. He just dropped the "e" for some reason. Some 35 years later, and after I was born, my mother discovered the correct spelling and insisted it be added back on.
Several years ago I was corresponding with a MINKE family in Santa Barbara, a family that previously resided in western Pennsylvania. I have lost tract of them, but they also descended from the MINKE family in Rosenthal.
Although MINKE is rare the family was not concentrated in Rosenthal and can be found elsewhere in Germany. Alsace-Lorraine is now part of France, although many of the villages have retained the Germanic names.