I mean schools that do not offer doctoral programs in that field and are ranked bottom quartile in usnews. Could this actively harm an application? Are there any mitigation measures one could take if so.
It will depend on a lot of things. Of course it is not going to be a big jet assist to your getting in to a big-name school. But it's not impossible.
Sometimes the less prestigious schools are not bad, they just don't shine quite as brightly. In Canada, for example, if you do very well in an undergrad physics degree from nearly any school you can usually get into a good graduate school. The profs all know eachother in their area and can recognize talent even if they are not quite up to the level of the more prestigious schools. Sometimes they are very good at the routine stuff but not up to speed on newer research topics. So if somebody comes through who "blows the doors off" in undergrad they can push him forward.
If the prof you did your masters under is quite good, then a recomondation from them may carry a lot of weight. This is especially true if that prof has discovered some strong talent in the past. And if their PhD supervisor is a prof in one of the big-name schools.
If you did unusually well in the degree and impressed a lot of people, it may also have weight. Finishing first in your class has "oomf" even if it's not a particularly prestigious school. Of course it means more from the top ranked school, but it's not nothing.
Most masters programs have some kind of project or report, maybe not a full thesis but at least a review kind of task. If you have such and it's in a topic that a prof at the big-name school is interested in, that will help. Search around the net to find out who does research in your topic.
Another thing that can put some shine on you is extra curricular activities. Especially when those activities relate to your chosen path in some way. I got some attention by writing computer programs in my own time and so being able to say I knew FORTRAN, C, assembly language for a PDP 11, and a couple others. Though those helped more with summer jobs than getting accepted for theoretical physics. If you were doing an experimental science degree of some kind then being able to work in a lab and not set the place on fire will give you some points.
Doing TA work can be a help. If you have some teaching skill it may be attractive to profs who hope to unload some of their undergrad teaching duties.