By the time of Wallenberg's arrival there were only 230,000 Jews remaining in Hungary. With fellow Swedish diplomat Per Anger,[28] he issued "protective passports" (German: Schutz-Pass), which identified the bearers as Swedish subjects awaiting repatriation and thus prevented their deportation. Although not legal, these documents looked official and were generally accepted by German and Hungarian authorities, who sometimes were also bribed.
Short answer: He made passports for them and they were allowed through.
(not sure if this is correct but i found it on wiki, not the best but sometimes can have good info.)
