Encourage letters acknowledging debt though they're not really valid (8)
I believe the answer is:
spurious
'acknowledging debt though they're not really valid' is the definition.
The definition suggests an adverb but the answer is not.
'encourage letters' is the wordplay.
'encourage' becomes 'spur' (spur can mean to encourage).
'letters' becomes 'ious' (I can't justify this - if you can you should give a lot more credence to this answer).
'spur'+'ious'='SPURIOUS'
Can you help me to learn more?
(Other definitions for spurious that I've seen before include "False, fake" , "Inauthentic" , "Contrived" , "fraudulent" , "deceitful!" .)