Removing genes with less than a correlation cut-off between two matrices
Nice data and good question.

It is called "outlier" analysis or the analysis of the residual. Its an easy analysis, but . You calculated the standard deviation using the regression slope as the 'mean' and retain data within 1.96 standard deviations. You can plot the data like this and if you are lucky will see the residual forming a nice 'normal distribution'. Outliers outside 1.96 sd can be formally excluded.

Calling (and plotting) the residual from the regression slope will be possible in R, but I use external packages because its easy. BTW you should also try Spearman's coefficient to check you are getting the same answer.