  In this paper, we consider the Gauss quadrature formulae corresponding to
some modifications of anyone of the four Chebyshev weights, considered by
Gautschi and Li in \cite{gauli}. As it is well known, in the case of analytic
integrands, the error of these quadrature formulas can be represented as a
contour integral with a complex kernel. We study the kernel, as it is often
considered, on elliptic contours with foci at the points $\mp 1$ and such that
the sum of semi-axes is $\rho>1$, of the mentioned quadrature formulas, and
derive some error bounds for them. In addition, we obtain, for the first time
as far as we know, a result about the behavior of the modulus of the
corresponding kernels on those ellipses in some cases. Numerical examples
checking the accuracy of such error bounds are included.
