Need to bring old H1 approval notices when apply TN?

When apply for TN, do I need to bring old H1/F1 approval notices with me, i.e. to prove that there is no gap in my previous stay in the US?

Thanks.

No, it should not be necessary. Your previous immigration status in F1/H1 would already be in the DHS computer and readily accessible by the applicable inspector. If they suspected you of an overstay or illegal presence, they would most likely examine your I-94 departure record for any inconsistencies.