Putze was the senior national officer in command of the New Zealand contingent in Sinai at the time.
White said Putze and Cappola had sex in March 2018, and entered into a "close personal relationship". She said the incident in March was "characterised by the accused as a one-night stand".
After returning to New Zealand, Putze was directly asked by Major General John Boswell whether he had entered into a relationship with Cappola.
He allegedly told Boswell he did not enter into any relationships with any members of his contingent.
White said the actions were likely to "prejudice discipline".
But defence counsel Commander Christopher Griggs slammed the allegations as "gossip, rumours, and innuendo".
He told the panel of military members most of the prosecution case was just that.
Opinion and hearsay was not admissible evidence, he said.
Even if the panel thought he was in a relationship, they had to be sure he knew he was in a relationship, he said.
There are 13 prosecution witnesses due to be called, including Cappola, Boswell, Putze's ex-wife, and Cappola's ex-husband.
The trial, which is taking place in Trentham, Upper Hutt, resumes tomorrow.