  Lattice paths in the quarter plane have led to a large and varied set of
results in recent years. One major project has been the classification of step
sets according to the properties of the corresponding generating functions, and
this has involved a variety of techniques, some highly intricate and
specialised. The famous Kreweras and reverse Kreweras walk models are two
particularly interesting models, as they are among the only four cases which
have algebraic generating functions.
  Here we investigate how the properties of the Kreweras and reverse Kreweras
models change when boundary interactions are introduced. That is, we associate
three real-valued weights $a,b,c$ with visits by the walks to the $x$-axis, the
$y$-axis and the origin $(0,0)$ respectively. These models were partially
solved in a recent paper by Beaton, Owczarek and Rechnitzer (2019). We apply
the algebraic kernel method to completely solve these two models. We find that
reverse Kreweras walks have an algebraic generating function for all $a,b,c$,
regardless of whether the walks are restricted to end at the origin or on one
of the axes, or may end anywhere at all. For Kreweras walks, the generating
function for walks returning to the origin is algebraic, but the other cases
are only D-finite. To our knowledge this is the first example of a
quarter-plane model with this property.
