The station was fined £20,000 in December for breaching impartiality rules after presenter James Whale urged listeners to vote for London mayoral candidate Boris Johnson.
Talksport pleaded that they had taken “swift and decisive” action to resolve the matter by dismissing Mr Gaunt and offering an on-air apology two weeks later.
It added it "totally accepts and regrets that the language was offensive and that the manner in which the interview was conducted was indefensible".
Mr Gaunt and Mr Stark had been discussing Redbridge Council's decision to prohibit smokers from fostering children when Gaunt called Mr Stark a "health Nazi" and an "ignorant pig".
Gaunt is a former BBC radio presenter, currently presenting an internet radio station for The Sun.