It's definitely a really difficult problems as the platform will attempt to compress and optimize the images.
You want to make sure that whatever image you are producing is compressed and optimized to the best that you can get it and as sharp as you can get it at that point. Often times when this is the case it will have limited compression artificates and distortion when further compression is performed by the webinar tool.
If you are making the images in something like Photoshop, savings for web and devices as a PNG if you have text in them is usually the best option. While it doesn't provide the maximum compression, PNGs preserve the clarity of the text better when compressed normally and saving for web in Photoshop will give you a pretty good idea of how the image will look when it's compressed a bit.