The problem of the best recovery in the sense of Sard of a linear functional $Lf$ on the basis of information $T(f)=\{L_jf,j=1,2,\ldots,N\}$ is studied. It is shown that in the class of bivariate functions with restricted $(n,m)$-derivative, known on the $(n,m)$-grid lines, the problem of the best recovery of a linear functional leads to the best approximation of $L(K_nK_m)$ in the space $S=\{L_j(Kn\overline{(K)}_m),j=1,2,\ldots,N\}$, where $K_n(x,t)=K(x,t)-L^x_n(K(.,t);x)$ is the difference between the truncated power kernel $K(x,t)=(x-t)^{n-1}_+/(n-1)!$ and its Lagrange interpolation formula. In particular, the best recovery of a bivariate function is considered, if scattered data points and blending grid are given. An algorithm is designed and realized using the software product MATLAB.