I would call a cloth that covers a ciborium a “ciborium veil”.
The liturgical book
Holy Communion and the Worship of the Eucharist Outside of Mass has in n. 19: “The eucharist for communion outside a church is to be carried in a pyx or other covered vessel; the vesture of the minister and the manner of carrying the eucharist should be appropriate and in accord with local circumstances.” Perhaps carrying a veiled ciborium is one of the methods in some places.
I would not regard the veiled ciborium on the altar during Mass as exposition of the blessed sacrament. It has in
Holy Communion and the Worship of the Eucharist Outside of Mass:
“83. During the exposition of the blessed sacrament, the celebration of Mass is prohibited in the body of the Church.”
An exception to this is made with the monstrance, but not with the ciborium, in this part:
“94. In the case of more solemn and lengthly exposition, the host should be consecrated in the Mass which immediately precedes the exposition and after communion should be placed in the monstrance upon the altar. The Mass ends with the prayer after communion, and the concluding rites are omitted. Before the priest leaves, he may place the blessed sacrament on the throne and incense it.”
The announcements are part of the concluding rites. So that they are happening is another indication that this is not exposition.
The General Instruction of the Roman Missal envisages vessels needing purification being covered with a cloth. It has in n. 163: “If the vessels are purified at the altar, they are carried to the credence table by a minister. Nevertheless, it is also permitted to leave vessels needing to be purified, especially if there are several, on a corporal, suitably covered, either on the altar or on the credence table, and to purify them immediately after Mass, after the Dismissal of the people.”
So if there is a covered ciborium on the altar during the announcements at Mass I would think it is an empty one awaiting purification.
The 1908 New Advent encyclopedia entry on Ciborium has: “While containing the Sacred Species it should be covered with a small white veil of silk or cloth of gold, and may not be handled except by sacred ministers; when empty and purified it may be touched by all clerics (Cong. of Rites, Jan., 1907), and by lay persons if specially authorized.”
[Morrisroe, P. (1908). Ciborium. In The Catholic Encyclopedia. New York: Robert Appleton Company. Retrieved November 18, 2019 from New Advent:
http://www.newadvent.org/cathen/03767a.htm ]
Dennis Smolarski S.J., wrote in Liturgical Literacy, that “special veils were formerly required when ciboria containing the consecrated bread were stored in tabernacles.” (Liturgical Literacy, 1990, published by Paulist Press, ISBN 0809131374, page 80.)
[Excerpts from the English translation of
Holy Communion and the Worship of the Eucharist Outside of Mass, © 1974 International Commission on English in the Liturgy Corporation. Excerpt from the English translation of
The Roman Missal, © 2010 International Commission on English in the Liturgy Corporation. All rights reserved.]