시간을 나타내는 months 뒤에 that이 올 수 있나요?

During those months that the original gray hair is growing back, it is normal for other hairs around it to turn gray on their own.
여기서 months는 시간을 나타내는데 when이나 during which 대신 that을 쓴 이유가 궁금해요.
during which도 가능한 표현인지 함께 알려주세요.