Оксфордский толковый говорит, что "надоедать", ни разу не травить. Urban dictionary говорит то же самое.
verb
to put pressure on sb by repeatedly asking them questions or asking them to do sth
Syn: ↑pester
• ~ sb (into doing sth) I finally badgered him into coming with us.
• ~ sb about sth Reporters constantly badger her about her private life.
• ~ sb to do sth His daughter was always badgering him to let her join the club.