According to various experts' opinion, there's no evidence of permanent damage, but temporary strain, yes, e.g. according to this University of California-Irvine page
A frequently made observation with screen-use in the dark is that it can strain one’s eyes. This is indeed true for many individuals and has been proven scientifically. The Lighting Research Center (LRC) conducted a study where two groups of participants were told to watch a movie in different settings of lighting. One group viewed an hour of the film in the dark first and then another hour of the film with wall illumination. The other group did the same, but just in the opposite order. As a result, the researchers discovered that less screen-use in poorly lit settings resulted in less frequent blink rates, less eyestrain, and less fatigue . [...]
However, these kinds of conditions are only temporary and have no severe effects on one’s eyes. [...] 
It cites a few references, and  (which is about strain) is a typical controlled study with two groups, but they are only citing a newspaper article for  which contains more expert opinion.
Dr Treacy told TheJournal.ie that the myth is grounded in attempts to get children to go to sleep, and because we grew up hearing it, it became a fact. Saying that looking at the screen of a smartphone, television, or laptop in the dark is bad for your eyes is simply the modern version.
It's a bit hard to prove a negative like this since eyesight does get worse with age. It would take at least one longitudinal study to be somewhat sure, but I don't know if one was done. Getting funding for a study like this is generally a problem when something is not likely/suspected [by experts] to be a problem.
There is one meta-analysis that suggest that (smartphone) screen over-use might result in various/worse visions problems sooner, a least in children. But extrapolating from that to other situations is quite iffy. (It's also not a great analysis, since it pooled over various conditions/afflictions.)