I think you've underestimated the value of his central contract, according to the mirror the value of an all formats central contract is £925,000 along with a £15,000 match fee per test (
https://www.mirror.co.uk/sport/cricket/how-much-englands-cricket-players-20020573) and there's only been talking of this going up with the suggestion that some all format players are now on £1m+. With those 2 tests being at homes at Lords (where Woakes had an insane record) and Birmingham (his home ground) and Stokes, Curran and Archer missing he'd have been a guaranteed starter in both those tests had he not gone to the IPL.
Assuming he'd have been away at the IPL about 8 weeks in total:
Central contract lost: (56/365)* £925,000 = £142k
Match fees lost: 2*£15,000 = £30k
Giving him a total loss from participating in the IPL of approximately £22k, along with the other personal factors of a couple of months away from home of course.
He'd be taxed on his earnings in India the same way he'd be taxed on his earnings in the UK.
The quarantine fees was an added point that I wasn't sure about (he'd have earnt more staying at home regardless of them), but have you got a source showing his franchise would've paid his quarantine fee on return to the UK though?