Hey Kathleen,
I am a little confused about the details of this request. I can see the Catharina Wink [Wenk-60] in your tree given as
Catharina Maria Louisa "Catherine, Kate" Munkelwitz formerly Wenk aka Wink
Born 29 Jan 1852 in Germany
So is this wrong or are you unsure? Just asking since you even have already parents attached, and I could not find a clue that gives you Bürgeln as place of birth.
Next mystery is the fact, that there is no Herman Wink born in Bürgeln in 1847. I even looked in to a plus/minus 7 Year timeframe. So I have no clue there the information in the other profil (Herman Wink) comes from. This is somethig that surely has to be double checked !!!
Nevertheless I can at least answer your question about the parents of Catharina Wink, born 1852 in Bürgeln: The record reads:
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[1852] geboren: 14. Januar, Abends neun Uhr; getauft: Ibid. 16. ejusd.: Katharina Wink, des Hermann Wink, Maurer, et ux. Katharina, geb. Hahn, Tochter; Taufpathen: Katharina, des Henrich Wink, Taglöhner, Ehefrau, geb. Ebert, des Vaters Bruders Frau.
Translation: born on January 14th, at 9 p.m., and baptizes on the 16th the same month: Katharina Wink, daugther of Hermann Wink, bricklayer, and his wife Katharina, née Hahn; godparent: Katharina, née Ebert, wife of Heinrich Wink, daylabourer, who is the brother of the childs father.
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source is to be found on archion.de under Landeskirchliches Archiv Kassel > MarburgLand > Bürgeln > Taufen 1830-1912; page 76.
Link: http://www.archion.de/p/a4dd4b17a6/
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Hope it helps. To do more it would take a lot of double checking and clearing up.