Did the client ask for a lower charge or did they contact you about cat care, knowing full well how much it would cost?
I would allow the entire booking to be charged at the holiday rate, but that is me. I would be insulted by anyone asking me to discount my services at a peak period. Also, the hotels and airlines do not differentiate. Anything after December [x date] is considered peak holiday.
However, there are many here who will modify the booking manually to lower the cost to their clients. That is how you can proceed because if it is broken down into two bookings, Rover will levy its service charge (up to $50) on each one.
Do whatever you think is fair and take into consideration whether these are repeat clients or have the potential to be in the future, although there are no guarantees. Also, you didn't specify if you were boarding the cat (which means it is taking up space in your home) or merely doing drop-ins for it. That can make a difference.