The phrase "reconstruction methods" refers to different techniques or approaches used to rebuild or restore something back to its original form or state. Full definition
Figure: Test of proxy climate reconstruction method with two climate models, HadCM3 and ECHO - G. (realclimate.org)
These arguably unrealistic features in the GKSS simulation make the simulation potentially inappropriate for use in testing climate reconstruction methods. (mustelid.blogspot.ru)
Smerdon, J. E., A. Kaplan, E. Zorita, J. F. González - Rouco, and M. N. Evans (2011), Spatial performance of four climate field reconstruction methods targeting the Common Era, Geophys. (eos.org)