Thanks for reaching out to Jotform Support. Unfortunately, it is not possible to remove the grey color in the selected option of the dropdown field. You can adjust the background of the selected dropdown field in your PDF via PDF Editor to download it. Let me show you how:
In PDFEditor, click on the Gearicon of the dropdown field.
On the right window that opens, under the DisplayStyle, you can change the Box color.
This is the output of the downloaded PDF:
Give it a try and let us know if you are looking for something else.