Why do mosquitoes appear to be repelled by magnets?
According to the research cited by the OP (Strickman et al. 2000), mosquitoes alter their behavior in the presence of a magnetic field, and the measured changes in behavior are statistically significant. The authors of the study found that the external surfaces of mosquitoes attract ferromagnetic particles from the air. They speculate that changing their orientation to the earth's magnetic field helps mosquitoes navigate while approaching a potential host.
Reference Cited
Strickman, D., Timberlake, B., Estrada-Franco, J, Weissman, M, Fenimore, PW, and R.J. Novak. 2000. Effects of magnetic fields on mosquitoes. Journal of the American Mosquito Control Association 16(2):131-137.