Is increasing the DPI of a low resolution image a good idea?
The comment you received is aimed at obtaining images of higher quality for publication.
Processing the files you sent them will not solve this issue.
If it did, the typesetters would already have done this themselves – this is what “insufficient quality to reproduce well” hints at.

In your specific case, the images seem to be digitalisations of historic photographs.
Thus, the only way to improve the quality is to obtain higher-resolution digitalisations of these photographs.
If you cannot do this, write exactly this to the publisher; they are most likely going to accept this.
Also note that if those images are test cases for some image-processing algorithm or similar, they should be printed exactly as they are, and this is what you should write the publisher.

The entire remark about the resolution probably doesn’t apply to you but was made for illustrations, plots, and similar.
These are almost always best provided in a vector format (which has infinite resolution, if you so wish) and even if using a pixel format, they can be produced at arbitrary resolution.
The resolution requirements are aimed at those researchers who insist on working with pixels in this case.