G. Villefranche has written:

'Thanksgiving after Holy Communion' -- subject(s): Lord's Supper, Catholic Church, Prayers and devotions

Yes, of course. It could be sung during the Preparation of the Gifts when the Bread and Wine are placed on the altar as the Priest prepares them for Holy Communion or it could be sung during the Distribution of Holy Communion to the Faithful or as a hymn during the Thanksgiving Period of Quiet Prayer after Holy Communion.

The Holy Eucharist, also known as Communion. It is widely taught that the word Eucharist itself means (thanksgiving) in Greek.

Catholics do not take communion, they receive communion.