Whether to check that the ideal is geometrically vertex decomposable using the result of [KR, Corollary 4.5] which relates the geometrically vertex decomposable and Cohen-Macaulay properties. Set CheckCM=>"once" to perform this check once (default, only for the ideal given in the input), CheckCM=>"always" check for the following $C_{y,I}$ and $N_{y,I}$ ideals as well, or CheckCM=>"never".
[KR] P. Klein and J. Rajchgot. Geometric Vertex Decomposition and Liaison. Forum of Math, Sigma, 9 (2021) e70:1-23.