Crossword Genius

Decline to take the dog back, but have to (2,4)

Ross

I believe the answer is:

go down

I'm a little stuck... Click here to teach me more about this clue!

'decline' is the definition.
(I know that decline can be written as go down)

'the dog back but have to' is the wordplay.
I cannot quite see how this works, but
an anagram of 'dog' is 'god' which is located in the answer.
'have' could be 'own' (to have something is to own it) and 'own' is found within the answer.
No letters remain.
This explanation may well be incorrect...

'to take' is the link.

Can you help me to learn more?

(Other definitions for go down that I've seen before include "Fall" , "Descend - be relegated" , "Subside" , "Decline" , "leave university" .)

I've seen this clue in the Evening Standard.
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