Admit to putting iron beside reclining cat (4,2)

'admit' is the definition.
(I know that fess up is a more specific form of the action concede)

'iron beside reclining cat' is the wordplay.
'iron' becomes 'fe' (Fe is the chemical symbol for iron).
'beside' is a charade indicator (letters next to each other) (I've seen this in other clues).
'reclining' says the letters should be written in reverse (recline can mean to move back).
'cat' becomes 'puss' (puss is a kind of cat).
'puss' reversed gives 'ssup'.
'fe'+'ssup'='FESS UP'

'to putting' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?