Step-by-step explanation:
In the sentence "Don't keep checking to see if the bleeding has stopped," the phrase "to see" is (C) an Infinitive.
Infinitives are verb forms that are typically preceded by the particle "to." In this sentence, "to see" functions as the purpose or intention of the action of checking. It expresses the reason why someone is checking. It functions as a noun in this sentence, serving as the direct object of the verb "keep."