Translation:The child does not want to help his parents with laying the table.
"The child doesn't want to help his parents with setting the table." should also be accepted
the sentence ought to read Barnet vil ikke hjaelpe sine foraeldre med at daekke bordET!
"Setting the table" is a fixed phrase, and it doesn't really have much to do with a certain table. "At dække bord" is also a fixed phrase. Bord is kinda part of the verb.
"Setting the table" should be an accepted translation of "at dække bord" ("den Tisch decken" in German). The current translation "laying the table" is also in use in Britain, see https://www.theguardian.com/lifeandstyle/wordofmouth/2009/dec/21/modern-manners-laying-christmas-table