  High-energy modifications to general relativity introduce changes to the
perturbations generated during inflation, and the latest high-precision
cosmological data can be used to place constraints on such modified inflation
models. Recently it was shown that Randall-Sundrum type braneworld inflation
leads to tighter constraints on quadratic and quartic potentials than in
general relativity. We investigate how this changes with a Gauss-Bonnet
correction term, which can be motivated by string theory. Randall-Sundrum
models preserve the standard consistency relation between the tensor spectral
index and the tensor-to-scalar ratio. The Gauss-Bonnet term breaks this
relation, and also modifies the dynamics and perturbation amplitudes at high
energies. We find that the Gauss-Bonnet term tends to soften the
Randall-Sundrum constraints. The observational compatibility of the quadratic
potential is strongly improved. For a broad range of energy scales, the quartic
potential is rescued from marginal rejection. Steep inflation driven by an
exponential potential is excluded in the Randall-Sundrum case, but the
Gauss-Bonnet term leads to marginal compatibility for sufficient e-folds.
