Hi Lisa,
Sorry for the delay. Starting at Gatwick in the peak is going to cost quite a bit, but there are ways to mitigate this. Assuming that your Oyster cards don’t have a railcard discount associated with them (ie you pay full adult fares) then I’d look to get them refunded while you’re in London. More on that below.
If you use a contactless card then you’ll cap more favourably, probably at the £7.70 zone 1-2 cap plus a single from Gatwick on top. Oyster would keep charging until you reached the cap from Gatwick, possibly as much as £35. On the second day it’s not so much of a problem because you’ll be limited by the zone 1-2 cap before heading to the Airport. Contactless adds up all your travel for the day and charges your bank one amount at the end, so no need to topup or worry about leaving too much on the card.
The peak single from Gatwick to Victoria (or Blackfriars or London Bridge) is £16.50. You can reduce this by splitting your journey at East Croydon. Gatwick to East Croydon is £5.70 peak and East Croydon to Victoria etc is also £5.70 peak, making a total of £11.40 or a saving of £5.10. If you have lots of luggage then it may seem a hassle, but that’s your call. Off-peak the saving is only £1.70 so may not be worth it. You need to touch out at the gates, go through and then touch back in going back into the station.
Finally back to refunding the Oyster cards. If they were purchased before 23rd February 2020 then there will be a £5 deposit on the card. After that date the £5 became a fee which is refunded as PAYG credit after 12 months. To get the fee refund you have to use the card to make a journey. This happens automatically for the first 6 months after the year anniversary, but you need to call the helpdesk first if it’s more than 6 months. If you are in this situation then you may want to call the helpdesk before you fly in and use the Oyster cards to make the Gatwick to East Croydon journey so you get the refund.
Then, if there is less than £10 credit on the card it can be refunded at a tube station ticket machine along with the deposit if there is one. If there’s more than £10 then you have to call the helpdesk and they will arrange a refund to your bank. More details at https://tfl.gov.uk/fares/refunds-and-replacements/oyster-pay-as-you-go-credit-no-longer-needed.
I hope this helps, but do please ask again if it’s not clear.