Hi NexusFX,
Welcome to the forums
I've downloaded your file and exported it as PDF, using the PDF (for export) preset exporting Artboard 1 only. Opening this PDF in Acrobat Pro automatically gives it a white page background, but this is not part of the file. If you open Acrobat Preferences (CTRL+K) and navigate to Page Display, then check 'Show Transparency Grid'. Now your PDF will display as it's been exported, without a background. I've attached the PDF I've created below: djp5klogossample.pdf
What program is your client using? It may be specific to their import procedure to keep the transparent background.
NexusFX reacted to Dan C in Cannot Export Vectors with Transparent Backgrounds