What happens if there’s an ongoing disagreement about whether content should appear on an entry?

The first step, during a declared COI proposal for a revision, is always to engage in a civil conversation with the editor with whom there is a disagreement. Sometimes these discussions can involve many more words than the length of the article or content in dispute.
If you try to take a short cut and add back (or remove) the content directly, you might end up in a ping-pong war. This will count against you if the article ends up in an administrative review. It can also get you banned.

The presumption of who’s in the right is initially in favor of the person without a COI. As soon as they disagree with you on an edit, the content is deemed controversial,. A discussion, group consensus, or administrative review needs to be requested. Arguments are marshaled pro and con the edit and consensus or the higher-ranking admin will decide. Generally, their decisions are fair. There are situations where discussions and votes are manipulated by editors with a hidden agenda. These are among the most difficult problems to deal with on Wikipedia and can require multiple rounds of review and appeal.