One of two ways to approach this. The first is to make the background match the color of your web page. This way is not as elegant if you change web backgrounds, or if you put it on various pages with different colors.
The second way would be a combination of things.
1.) make a second copy of your completed logo. Make this a new object. Sometimes pasting this object into a new layout can help with unwanted jaggies. This can also help make your pallette selective - if you begin the new layout with an 8bit pallete. Also, make sure your background has no variations onf the "blue" pallete - go with something with a very low blue content - something contrasty and opposite side of the color wheel - yellowish if I have to guess (but be careful of any whites). Possibly even something in the reds.
2.) when you export your gif, be sure to select the "optimized" or "adaptive" color pallete choices. Both have had good luck for me in the past.
3.) When you create your mask around the object, try not to feather it, as this gives a semi transparent edge to the mask. You would be better off with 0 transparency, and 0 feathering. This gives a nice clean crisp edge. If you can get away with it, you would be better off REDUCING the mask by 1 pixel (inside). This will cut off the outter most layer of pixels from the mask, and cut your logo as close as possible to ensure no background "artifacts".
These tips should get you a much cleaner final output. The biggest two things you can do is select a contrasting background color instead of no background, and get that logo object duplicated, and have a distinct background and a seperate logo. This will help insure that the two are not blending somewhere along the line - especially with a transparent background - it can be hard to see any "smoothing" areas that the mask might pick up.
I am sorry I cant give you more precise directions, as I haven't used version 9 in so long now, it is hard to remember which options it had and which it didnt. There are some good version 8, 9 and 10 tutroials on the web though. Google Corel Photo paint tutorials, and you get a good list. Here are a few:
The reason I recommend these are they have specific directions of EXACTLY which menu/tool options to select. Some of the techniques may be below you, but you can find the specifics here that might help.
This last one (below) will be of particular benefit, since it goes over the details of gif images in depth. However, I beleive this a version 8 tutorial, so there may be some slightly different methods of accomplishing the same tasks, as 9 had some pretty major changes over 8, but the theory will be the same.
Let me know if there is anything else I can help you with.