All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Talking to one's family on the phone while observing i‘tikaaf in the mosque so as to check upon them involves no sin, even if he calls them from inside the mosque. Safiyyah said: “The Prophet, sallallaahu ‘alayhi wa sallam, was observing i’tikaaf in the mosque. I visited him at night and we both talked. When I got up to leave he got up too...” [Al-Bukhari and Muslim] The Hadeeth implies that the one who is observing i‘tikaaf may talk with his family even from inside the mosque. In his book Al-Mughni, Ibn Qudaamah says, “It is allowed to talk with others as needed while observing i‘tikaaf.”
That being said, there is nothing wrong with talking to one's family to check upon them when observing i‘tikaaf. This does not invalidate i’tikaaf. Nevertheless, one is encouraged to spend his time worshipping Allaah and avoid all that which he is not concerned with.
Allaah Knows best.