\begin{pgfonlayer}{back}
\makeatletter
\pgf@matrix@offset
\pgfgetlastxy\ck@shift@x\ck@shift@y
\begin{scope}[shift={(\ck@shift@x,\ck@shift@y+0.3333em)}]
\foreach \row in {1,...,4} {
\foreach \col in {1,...,4} {
\pgfmathparse{Mod(\row + \col,2) ? "red" : "blue"}
\colorlet{sqbg}{\pgfmathresult}
\fill[sqbg]
(\csname pgf@matrix@minx\col\endcsname - \csname pgf@matrix@maxx\col\endcsname, \csname pgf@matrix@miny\row\endcsname - \csname pgf@matrix@maxy\row\endcsname)