Can I attempt to get rid of my Cursed condition on the same reckoning phase that a Warlock inflicts me?
Page 10 of the Rulebook:


  Resolve these effects in the following order: Monsters, Ancient One sheet, Ongoing Mythos cards, and lastly investigator possessions and Conditions.


Would suggest that you can, however, in the Reference Guide it states:


  If a Monster is spawned or an investigator gains a component while investigators are resolving reckoning effects, they do not resolve the reckoning effect on that Monster or component.


Since cards are components, you cannot get rid of it on this turn.