Hi,
This is because the note is showing the modified on date rather than the created on date - when you re-assign the quote, there is a parental relationship to the note entity so that the note is also re-assigned - hence changing the modified on date. If you don't wan this to happen, you can change the 1:N relationship from Quote->Note to configurable cascading and change assign to 'none'. You do need to be aware that this will mean that if you have security roles with anything less than organisation level privileges on notes, some users may not be able to access the notes when the quote is assigned to them.
hth