  Let W be the number of points in (0,t] of a stationary finite-state Markov
renewal point process. We derive a bound for the total variation distance
between the distribution of W and a compound Poisson distribution. For any
nonnegative random variable \zeta, we construct a ``strong memoryless time''
\hat \zeta such that \zeta-t is exponentially distributed conditional on {\hat
\zeta\leq t, \zeta>t}, for each t. This is used to embed the Markov renewal
point process into another such process whose state space contains a frequently
observed state which represents loss of memory in the original process. We then
write W as the accumulated reward of an embedded renewal reward process, and
use a compound Poisson approximation error bound for this quantity by
Erhardsson. For a renewal process, the bound depends in a simple way on the
first two moments of the interrenewal time distribution, and on two constants
obtained from the Radon-Nikodym derivative of the interrenewal time
distribution with respect to an exponential distribution.
  For a Poisson process, the bound is 0.
