Inkscape's default is to save SVGs without any background, unless you added one.
Try dragging your SVG into a raster image editor like GIMP or Photoshop. You'll soon find out if it really has a background or not. If it does, then either you added it, or your printer's website has done something to the image.
Here's a screenshot of a basic SVG, a circle with a fill and stroke, created in Inkscape, with default settings, and opened directly in GIMP. There is no background. The same is possible with Photohsop.
Here is the link to download this SVG if you want to try it yourself. http://www.filedropper.com/test_305