There is a possibility that pronunciation and spelling errors may have crept in. (There is a major spelling error in the family name of my mother's side of the family, which I uncovered and which has greatly complicated tracing family roots on that side.) There are several varients of the surname. In North America, Teske is usually pronounced TESS-key, strong accent on the first syllable. With one exception I have always heard people with the name pronounce it with two syllables. There was one person I ran across who pronounced it Tesk with a silent e. (Though I get it many times that way here in Maryland where the name is quite uncommon. I'm from Wisconsin originally and while not the most common name, people to tend to pronounce in correctly. In Germany, however, it is pronounced TESS-kuh.
There is one varient Teskey seen in North America (but never in Germany) and that seems to be from one group of Germans who moves to Ireland in the 18th century, stayed there for about 50 years and then emigrated to North America (mostly to the prairie provinces of Canada which spells it with a "y". They may have added that "y" just to emphasize that the name doesn't have a silent "e" at the end. The use of the letter "a" in place of the first "e" may simply have been a handwriting error. German cursive script in the 19th century was quite different from English cursive. Many records were handwritten in a now obsolete cursive style. Present German is pretty much written with standard Roman cursive writing. Quite a few German names have the -ske ending which is one of the German patronymic forms(equivalent to the Polish -ski or the Russian -sky" meaning "son of".) Another is -sohn...as in the composer Mendelssohn, "son of Mendel" which in this case was a Jewish name. The composer Mendelssohn's father was a convert to to Christianity. By some circuitous linguistics Teske is derived, according to German philologists, from "son of Matthew" [In German Mathis or Matheus, one is the Evangelist the other a Disciple, a spelling distinction not made in English]. Most Teske's seem to come from the Northern Prussian provinces of Posen, Pommerania, and Mecklinburg where there were Germans of Slavic extraction. There are about 50 German surnames derived from this Mathis/Matheus root that begin with the letter "T." My sources for this are two German book from the 1930's (when Germans were quite concerned of what their family root were or more particularly what they were not, specifically Jewish.) One of those books was called Unser Famillienomen (Our Family Names) which I found in the library of my US Gov't Intelligence Agency during my career there (I'm now retired.) For much of my early career, I was a cryptlogic linguist and as such took great interest in languages, names and varient names.
So in answer to your question...it is a definite "maybe."