I have Web Credit in my account but the only option appears to be to redeem it to my bank. Can I transfer it to my Oyster card somehow?
Yes, you can "transfer" web credits to your Oyster by purchasing pay as you go credit online using the web credits, in part or in full.
The Transport for London's terms and conditions for online accounts states:
Section 6 - Web credits
- You can choose to have certain types of refund or goodwill payments credited to your account as web credits. Any balance accrued can be used as part or full payment when you buy pay as you go credit or Travelcards.
You can do so in your Contactless and Oyster account by picking the Oyster card you want to top up and choosing "Top up or buy season ticket":
When you click Next page, the web credit is automatically applied. All you need to do is to pay for any shortfall you might have:
(Images mine, credits to the OP for reminding me that I have a few quid sitting in my Oyster account!)