The answer to your question is easy but profoundly important; it takes us to the heart of the gospel. There is no place in the Orthodox Presbyterian Church, or in any church true to Scripture, for altar cloths because there is no place for an altar of any kind.
The table used for celebrating the Lord's Supper is just that, a family table before or around which the congregation gathers for a meal as God's children. It is a table for communion with the ascended Christ, not an altar where he is in some sense re-sacrificed or his sacrifice "re-presented" to God.
Christ's sacrifice for sin has a once-for-all finality and sufficiency (see, for example, Heb. 7:27; 9:12, 26; 10:10). Because of that sufficiency and finality, an altar—and so an altar cloth of any sort—is excluded from the worship of God's people that would be "in spirit and truth" (John 4:24).
I hope this reply will be of help to you.
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