Depending on the time reference we’re talking about we can use the Verb in past and ある in present, or both the Verb and ある in past.

見たことがありません or 見たことがありませんでした

1. 見たことがありません (mita koto ga arimasen):
   • This expression is in the present tense and indicates that you have not seen or experienced something up to the current moment.
   • Example: "その映画を見たことがありません" (Sono eiga o mita koto ga arimasen) means "I have not seen that movie."
2. 見たことがありませんでした (mita koto ga arimasen deshita):
   • This expression is in the past tense and implies that you had not seen or experienced something up until a certain point in the past.
   • Example: "昨日まで、その映画を見たことがありませんでした" (Kinou made, sono eiga o mita koto ga arimasen deshita) means "Until yesterday, I had not seen that movie."

Choose the form that aligns with the timeframe you want to convey. If you're discussing experiences up to the present moment, use the present tense ("見たことがありません"). If you're referring to experiences up to a specific point in the past, use the past tense ("見たことがありませんでした").