The correct option is B Had I known about his true intentions
An adverb clause is a group of words containing a subject and a verb,
and it functions as an adverb, by modifying an adjective, verb or an
adverb. Adverb clauses generally begin with a subordinate conjunction
(since, because, while, etc.).
Option C is correct because it is an
adverb clause of condition, 'had' refers to a condition, it means 'if I had known...'.
Option A is incorrect because it is an adverb clause of concession or contrast, 'though' is a conjunction used when two ideas contrast each other. Here they don't.
Similarly, option B is incorrect because it is an adverb clause of cause or reason, the option when added does not form a complete meaning.
Option D is incorrect because the answer lies in C.