When using the New Publishing tool, you can rearrange, hide and delete columns when reviewing or adding data to your dataset. You will first need to create a revision of your dataset using the action bar.
Once in the new tool, you will first want to select either Add Data or Review Data, based on the action you will take.
This will load the columns in your dataset. Once loaded you can select the kabob in the right-hand corner of the column. This will provide all of the options you can take on your dataset.
The column order you see when reviewing data will be the same order as the published dataset. In order to move the position of a column in the dataset, you can use the Move Left and Move Right options to position the column where you would like it in the dataset.
To hide a column from the dataset view, simply open that same menu and select Hide Column. Hiding a column from the dataset can be undone in further revisions.
Finally, you can also use the Remove Column option to not include it in your dataset at all. Choosing this option will completely remove the column from the dataset. If you would like to include the dataset in further updates, you will have to add the column back to the dataset.