A contact modified on the Android device is not synchronized to Thunderbird
If you modify a field in a contact on the Android device and this contact is not synchronized to Thunderbird, check that this contact is not linked to several accounts. Therefore the same contact could be aggregated from a contact from a local account, from a Google account and from a Facebook account (for instance if they have the same name). It means that the different fields of the displayed contact could belong to different accounts. If this field belongs to an account that you didn't select to be synchronized in BirdieSync options on the Android device, then the contact will not be considered as modified and will be not synchronized. But note that if several accounts are selected to be synchronized on your Android device in BirdieSync options, it may lead to several instances of the same contact in Thunderbird, since there is no aggregation or link mechanism in Thunderbird.