Abstract: We apply the string-inspired worldline formalism to amplitudes in Scalar QED involving open scalar lines, and in particular to the study of their nonperturbative gauge-dependence. At the tree-level, we obtain a compact Bern-Kosower type master formula for linear and nonlinear Compton scattering with an arbitrary number of photons, on- and off-shell. At one-loop we rederive, in an efficient way, the off-shell vertex in an arbitrary dimension and any covariant gauge. Generalizing the Landau-Khalatnikov-Fradkin transformation for the nonperturbative propagator, we find simple nonperturbative transformation rules for arbitrary x-space amplitudes under a change of the covariant gauge parameter in terms of conformal cross ratios.