Quality of an image for publication reproduced from another source
It is difficult to provide a detailed reply without knowing more about the figure, for example if it is a photograph or a line graph. I will therefore concentrate on the general aspects.

First, the best would be if you could get some form of original from the author (or whoever) has the copyright). Screen dumps are clearly not sufficient since printing requires high resolution (300 dpi in final reproduction size is a commonly quoted resolution in journals)

Second, if it is a line graph, and it sounds as if that is the case, I would argue that the best way is to put the image in the background of a vector-based drawing program such as Inkscape/Illustrator/Corel Draw and manually redraw the figure. This is done by placing the illustration in a background layer and then draw lines in the program to reproduce the background. This requires learning a vector-based software and is a tough solution for the short-term but one I strongly recommend for the long-term. If the plot is based on data, for example a scatter graph, then you could digitize the data and re-plot it as long as you think of the re-plot as a version of the original plot and not use data points for additional analysis.

There are of course numerous kinds of complicated plots where the second approach will not work so trying to get the source would be the first choice. Screen dump quality bitmaps will be rejected by most if not all journals.