Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, thank you for your question that reflects a truthful desire to have a clearer view of the teachings of Islam. May Allah crown this truthful desire with His satisfaction and reward.
Primarily, there is nothing wrong with sending greeting cards for the `Eid to relatives and friends with phrases such as “`Eid Mubarak” and “Taqaballa Allahu Minna wa Minkum” (may Allah accept from you and us good deeds), as such greetings are part of customs, and permissibility is the original rule governing such customs as long as they don't violate the Islamic Shari`ah.
Here, we would like to cite for you the following Fatwa issued by Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, who states the following:
There is nothing wrong with greeting one another on the eve of happy religious occasions such as the coming of Ramadan, `eid, or the like. Rather, this may amount to Sunnah if it is meant to please another Muslim and to share the happy religious occasion with him. It is reported that the Prophet (peace and blessings be upon him) was asked: “Which act is better?” He replied, “To enter pleasure on a believer.” (Reported by At-Tabarani and others.) Also, it is well proven that good intention turns custom into an act of worship.
Now, it is clear, dear brother, that there is nothing wrong in sending `eid cards to felicitate your mother for the `eid. Rather, it is recommendable and you will be generously rewarded for keeping good relations with her.
Sending such cards is part of the custom of people and the act itself is based on the original rule of permissibility as long as their content doesn't contradict with the teachings of Islam.