SeedRandom[10801];
dimension = 5;
coDimension = 10;
percProbability = 0.7;
deleteMe =
Pick[Table[i, {i, 1, 30}], Table[RandomReal[] > 0.5, {i, 30}]]
G = GridGraph[{dimension, coDimension}, VertexLabels -> "Name",
ImagePadding -> 30]
(*H=SetProperty[VertexDelete[g,#],VertexCoordinates\[Rule]Delete[\
GraphEmbedding[g],#]]&@@deleteMe*)
n = 1; H = G;
While[n < Length[deleteMe], H = VertexDelete[H, deleteMe[n]]; n++]
H = SetProperty[H, VertexCoordinates -> GraphEmbedding[G]]