You can't hide the background.
When you published your .swf it sounds like you published it with a white background.
Unfortunately .swfs don't support having a transparent background, so you have to set the background colour you want. You can either do this at publish time or dynamically at runtime.
I'm assuming you're diplaying this on a web page and you want the background to be the same colour as the web-page. To do this you have two options: Option 1
Reopen your .fla, set the background colour of the .swf to the colour you're using on your HTML page and re-publish your .swf. OR Option 2
In your HTML, where you are embedding your swf, you can pass a parameter to set the background colour of the .swf at runtime.
So in your embed tags, you can set the background colour like this:
The above would set the background to black and set the width and height of the swf to be 800x600.
Changing the value of bgcolor to "#ff0000" would set the background to red.
If your HTML page is a light orange, perhaps "#ffb642", then simply set the bgcolor parameter to "#ffb642" and the background of the .swf will appear light orange.
If you're using a .js script (like swfobj.js) to embed your .swf in your HTML page then take a look at the documentation for the script, you should be able to find out how to pass parameters like bgcolor to the swf.
Either way, that should solve your problem for you!
Cheers for now,
Attached is a quick example to show you what I mean.
I've attached example.zip which contains a simple 200x50 .swf with an example of that text effect from the tutorial you posted. (example.swf)
The .swf has been exported with a white background, so it should be very similar to what you've currently got.
I've also included a very rough (and very orange) html file (example.html) which I knocked up in a few short minutes to show you what I was talking about in my previous post...There's no nice css or formatting in there or anything I just threw this together really quickly, so apologies if it is ugly to look at!
All it does is embed three instances of example.swf on the page.
The first instance has no bgcolor parameter in the embed tags, so it appears white. The second has had it's bgcolor parameter set to red, and the third is set to orange (so it blends in nicely with the rest of the page!)