Is expiation incumbent upon someone who said, "By God, I miss seeing you," as a courtesy and did not intend to make a vow?

The oath mentioned is a "ghamūs" (perjured) oath if you intended to make a binding oath, because it is an oath taken on something you know to be false. There is no expiation for it according to the majority of scholars; rather, what is obligatory is repentance and seeking forgiveness, because its gravity is too immense to be expiated. The Shāfi‘īs, however, hold that expiation is necessary for it, along with repentance and seeking forgiveness. However, if you did not intend to make a binding oath and the words merely slipped from your tongue unintentionally, then you bear the sin of lying, but not the sin of the oath. This is considered a "laghw" (frivolous) oath, for which there is no sin or expiation.