Dyche moved for Hart after Pope sustained a shoulder injury, seeing him join Heaton in the treatment room, while Lindegaard has also struggled with a thigh problem.
After seeing his summer purchase keep clean sheets in his first two matches, with Burnley playing out goalless draws against Istanbul Basaksehir and Southampton, Dyche has again defended the club's decision to sign Hart.
"Given the situation as it came around with the injuries that we had in the goalkeeping department," he told reporters at Wednesday's press conference. "I cannot understand the debate at all. It is pretty simplistic.
"[It was a] random injury to Nick Pope, the one last year to Tom which started off a longer process, Anders goes down with a thigh injury, it is not rocket science.
"The only difference is that we signed Joe and it was not a loan, but I am pleased with the business. Why would you not want a competitive unit? And all very good in my opinion."
Hart is expected to retain his place in the side for Thursday's Europa League third-round qualifier second leg against Istanbul Basaksehir.