What's the meaning of endorse here?
A visa is a document showing that a person is authorized to enter the territory for which it was issued, subject to permission of an immigration official at the time of actual entry. The authorization may be a document, but more commonly it is a stamp endorsed in the applicant's passport.
The closest definition I find from AHD is: to place (one's signature), as on a contract, to indicate approval of its contents or terms.
Could it also be applied here?