Hello @Marie-LouLabuschagne,
Thanks for raising this, we are working on a fix. The fix would be to honour the pop-up field settings rather than displaying the whole table or raw data. Most likely, the fix will be included in the upcoming patch.
As a workaround, try adding that layer through Data sources and whitelist the fields required. Essentially you have to add your Portal or AGOL as a data provider and then the layer needed for search as a data source. While configuring this, you will have an option to whitelist the fields as required. Once this is done, this data source can be used while setting up a search. Hope this helps.