With the rewrite_indices
which is now in the version on github, you can do
{a, b, c, d, e, f}::Indices(position=fixed).
\eta_{a b}::Metric.
ex:=F_{a}^{b} G_{b c} + F^{b d}G_{d a c b};
rewrite_indices(_, $F_{a b}$, $\eta^{a b}$);
This inserts as many ηab (with the right indices) as necessary in order to rewrite the expression using Fab (with lower indices) only.
Note the position of the indices in the rewrite_indices
algorithm: the first argument should give the tensor with the indices in the position in which you want to have them, the second argument is the metric/conversion tensor which you want to use for this. The names of the indices on these two arguments does not matter (just use the right index type).