The correct option is
D seeing
The given sentence already contains a main verb 'can't'. Thus, the answer must be a non finite verb. Further, the words 'can't remember' suggests that the action was real but the subject does not remember about it. Thus, the answer must suggest that the action was real.
Option A is incorrect. 'to see' is a non finite verb of the infinitive form, but infinitives are generally used to indicate abstract and unreal action and they do not suggest that the subject's action was real. Thus, it is not the correct answer.
Option B is incorrect. 'if I see' contains a conjunction. Thus, the presence of a verb is not incorrect, but, since, the action of having seen the girl is complete, the main verb must be in the present perfect tense(not past tense because the rest of the sentence is in the present tense). Thus, the answer is incorrect.
Option C is correct. 'seeing' is a non finite verb of the gerund form. Gerunds are generally used to indicate real action. Thus, it suggests that the subject's action is real and is the correct.
Option D is incorrect. 'did I see' does not contain a conjunction but contains a main verb. Having two main verbs in one sentence will make it grammatically incorrect.