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Mrs. Smith asked if there was anything good on (без артикля!) TV that night.
Mr. Smith ANSWERED that there was an interesting film on (без артикля!) channel 4 that evening.
Примечание.
To answer - отвечать на заданный вопрос, давать конкретный ответ;
to reply - говорить что-либо в ответ, реагировать на слова.
В данном случае - answer.
Mrs Smith said that she DIDNʹT WANT (=WAS NOT GOING) to miss her fitness CLASS and asked HER HUSBAND (избегаем повторения) to record THAT FILM (записать фильм, а не снять видео).
Mr. Smith agreed.
Mrs. Smith warned HIM NOT TO FORGET TO turn off the TV before he went to bed.

..the video for her .Mr Smith agreed. Mrs Smith warned Mr Smith to turn off the TV before he went to bed.

Mrs. Smith asked if there was anything good on the TV that night. Mr. Smith replied to Mrs. Smith that there was an interesting film on the channel 4 that evening. Mrs Smith said to Mr. Smith that she wouldn't like to miss her fitness club and asked him to record the video for her. Mr. Smith told her that he agreed. Mrs. Smith warned Mr. Smith that he would turn the TV off before he went to bed.