If you know that you have blown a tyre, best option is to leave gear down. But maybe you don't realise it in time to delay the gear retraction, as that is something that is instinctive to do on every takeoff. Often, the first indication will be when ATC call you to tell you that you left a trail of shredded rubber on the runway and what is the address to bill your company for the clean-up. If you are not losing hydraulics and there's no other indication of damage, you now want the weight as low as possible for a full flap landing, so the decision to return or continue is one of airmanship, fuel available etc. On the other hand if you are getting ugly warnings on the flight deck, to hell with the landing weight. Better a buggered landing gear on the ground than a fire in the air.