  Time-reversal invariant topological superconductors are characterized by the
presence of Majorana Kramers pairs localized at defects. One of the transport
signatures of Majorana Kramers pairs is the quantized differential conductance
of $4e^2/h$ when such a one-dimensional superconductor is coupled to a
normal-metal lead. The resonant Andreev reflection, responsible for this
phenomenon, can be understood as the boundary condition change for lead
electrons at low energies. In this paper, we study the stability of the Andreev
reflection fixed point with respect to electron-electron interactions in the
Luttinger liquid. We first calculate the phase diagram for the Luttinger
liquid-Majorana Kramers pair junction and show that its low-energy properties
are determined by Andreev reflection scattering processes in the spin-triplet
channel, i.e. the corresponding Andreev boundary conditions are similar to that
in a spin-triplet superconductor - normal lead junction. We also study here a
quantum dot coupled to a normal lead and a Majorana Kramers pair and
investigate the effect of local repulsive interactions leading to an interplay
between Kondo and Majorana correlations. Using a combination of renormalization
group analysis and slave-boson mean-field theory, we show that the system flows
to a new fixed point which is controlled by the Majorana interaction rather
than the Kondo coupling. This Majorana fixed point is characterized by
correlations between the localized spin and the fermion parity of each spin
sector of the topological superconductor. We investigate the stability of the
Majorana phase with respect to Gaussian fluctuations.
