Road lettering? That's the rumour (4,2,3,6)

'road lettering? that's the rumour' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'road lettering? that's the rumour' is the wordplay.
I cannot quite understand how this works, but
'road' could be 'street' (street is a kind of road) and 'street' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
'rumour' could be 'word' (the word on the street) and 'word' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?