The word "counter-sign" refers to the act of signing a document or agreement as a witness or co-signer. Some possible antonyms for this word might include words such as "oppose," "reject," or "dispute," which denote a disagreement or a lack of support for an action or statement. Other antonyms could include "ignore," "avoid," or "dismiss," which suggest a deliberate choice not to acknowledge or engage with a particular issue. Finally, antonyms such as "abstain," "refrain," or "forbear" may imply a sense of restraint, indicating a decision not to participate in a given action or to hold back from endorsing or supporting it.