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Using data from the Large European Array for Pulsars (LEAP), and the Effelsberg telescope, we study the scintillation parameters of the millisecond pulsar J0613-0200 over a 7 year timespan. The "secondary spectrum" -- the 2D power spectrum of scintillation -- presents the scattered power as a function of time delay, and contains the relative velocities of the pulsar, observer, and scattering material. We detect a persistent parabolic scintillation arc, suggesting scattering is dominated by a thin, anisotropic region. The scattering is poorly described by a simple exponential tail, with excess power at high delays; we measure significant, detectable scattered power at times out to $\sim 5 μs$, and measure the bulk scattering delay to be between 50 to 200\,ns with particularly strong scattering throughout 2013. These delays are too small to detect a change of the pulse profile shape, yet they would change the times-of-arrival as measured through pulsar timing. The arc curvature varies annually, and is well fit by a one-dimensional scattering screen $\sim 40\%$ of the way towards the pulsar, with a changing orientation during the increased scattering in 2013. Effects of uncorrected scattering will introduce time delays correlated over time in individual pulsars, and may need to be considered in gravitational wave analyses. Pulsar timing programs would benefit from simultaneously recording in a way that scintillation can be resolved, in order to monitor the variable time delays caused by multipath propagation.