Your image appears to be large enough to display well on a (non-retina) computer monitor. However, printed documents usually have many more points per inch than computer displays. An image that is just large enough to work on-screen is woefully small for print. Try an image file at least 3 times larger than the container field object you display it in.
I agree if you have an image that is actually larger you will be looking good. Do not confuse this with image better quality via image compression. It you just make the image "better quality" you may get something 30-40kb but will look just as bad. Without seeing the original image it is hard to say for sure.
I am confused as the detial you have is a 545x108 image and the attachment shows 570x36.
With printing you have to be concerned with the pixels or dots per inch. You put a larger image into the layout. Say 1090x216 or 1635x324 (double or triple as previously recommended), but you size it down on the layout. This is a big picture in a small box idea. This will allow the print to look even better. Many computer images run 72-100dpi and look fine. Decent printers like around 300dpi and many easily do 600dpi or more. You will eventually find a happy balance between image size and compression quality for your case.
What bigtom says. If you consider that screen resolution is 72ppi and print resolution is 300dpi, then you need images to be around 4 times the pixels displayed on screen (300/72 = 4.17) in order to print well. For example, a page header I use is printed in a field 119pt high, but the image used is 383pixels high.
Thanks all for this useful advice.
One thing I found is that FM will automatically generate a low-res thumbnail of the image when printing. You can turn this off in Manage > Containers > Thumbnails and turn off "Generate and store thumbnails for images."
But a word of caution. If you solution is image-heavy, turning this off can slow the performance quite a bit.
Unfortunately, I don't know of a way to alter this on a per-field or a per-layout basis. It seems to only be global for the entire file. I wish you could set this at the layout level for print layouts, and leave it on for other places where the performance gains would be beneficial.