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The densely populated Bay of Bengal (BoB) rim witnesses the deadliest tropical cyclones (TCs) globally, before and after the summer monsoon. Previous studies indicated that enhanced salinity and reduced thermal stratification reduce cooling under BoB TCs after the monsoon, suggesting that air-sea coupling may favor stronger TCs during that season. Using observations and simulations from a one fourth degree regional ocean-atmosphere model, we show that BoB TCs are stronger before the monsoon due to a more favorable large-scale background state (less vertical wind shear and higher sea surface temperature). Air-sea coupling however alleviates this background state influence, by reducing the number of premonsoon intense TCs, because of larger cooling and reduced upward enthalpy fluxes below TCs during that season. As the impact of air-sea interactions on BoB TCs is largest for intense TCs, it should be further investigated for Category 3 and above TCs, which are not reproduced at one fourth degree resolution.