This would be best translated into:
He thinks however he wants to think, I don't care.
This sentence structure is often used with 什么.
Word by word: You want to eat whatever, just eat whatever.
...which really means: Eat whatever you want.
This structure can work with any normal question pronoun
(wherever, whatever, however, whoever, whenever, for whatever...)
Here, 就 is pretty much equivalent to 'just', as in 'just do it'. It's not absolutely required here, but it's used very often.
You could write this type of sentence in Chinese more similarly to English:
你就吃你想吃的 (You just eat what you want to eat).
I think a native speaker would more inclined to use the xxxx什么就xxxx什么 structure, however.
See if you can wrap your head around this: