  A quantum spin Hall strip where different edges are contacted by $s$-wave
superconductors with a phase difference $\phi$ supports Majorana bound states
protected by time-reversal symmetry. We study signatures of these states in a
four-terminal setup where two Josephson junctions are built on opposite edges
of the strip and the phase difference between superconductors can be controlled
by an external flux. Applying a voltage bias across the quantum spin Hall strip
results in a sequence of conductance peaks from multiple Andreev reflections.
We find that this so-called subharmonic gap structure is very sensitive to the
phase difference and displays a phase-controlled even-odd effect, where all odd
spikes disappear when the Majorana states are formed for $\phi=\pi$. Moreover,
the remaining even spikes split when the superconductors forming the junction
have different gap size. We explain these features by showing that any midgap
bound states enhance the transmission of the even order multiple Andreev
reflections, while the reduced density of states at the gap edges suppresses
the odd order ones.
