The bottom line answer is “yes, you can fix it”. How you fix it will depend on the tools you have at hand. I don’t know how the particular Barz stack work. It asks for a YouTube URL, but does it also ask you to put in a “poster” image? That’s what we are seeing. Lots of stacks don’t do that, they just use the poster image supplied by YouTube.
So if you can supply your own poster image then there are ways to probably get better quality. If it uses the image used by YouTube then you may be limited by the original/big size of the video when uploaded. If, for example, a video has a maximum width of 640, but the poster image developed is bigger then there will be degradation in the image quality. So one solution would be to make sure the width of the video on your web page does not exceed the biggest width size at YouTube.
Some services like Vimeo allow you to choose what frame will be your poster image. That’s another possibility is to choose a different poster.