The word "whose" is spelled incorrectly in the sentence. It should be "who's," as it is a contraction of "who is" and refers to the woman's strong political views. Jack met a woman who's well known for her strong political views.
Here's why:
Whose is the possessive form of the relative pronoun who.
In this sentence, whose modifies the noun woman. It refers back to the woman Jack met and indicates that her being well known is related to her strong political views.
The adjective phrase well known for her strong political views describes the specific characteristic of the woman that makes her well-known.
Here is the corrected sentence:
Jack met a woman who's well known for her strong political views.