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The quality of CVD-grown graphene is intimately linked to the morphology of the employed catalyst. One commonly employed route to enhanced catalyst quality is recrystallization prior to graphene growth. The dimensions of a catalyst's single-crystalline domains, however, are limited by the stability of dislocations at the grain boundaries. We here employ a solid material in contact with the catalyst as a sink for dislocations. It was found that the interaction between Cu-foil and a solid cap significantly alters the recrystallization kinetics and achievable grain size. This development originates from an improved strain-relaxation of up to 1% during recrystallization which can support the formation of commonly unstable surface orientations. Correlation of diffraction measurements and atomic force microscopy reveals a direct impact of the strain relaxation on the decrease in copper surface roughness. Finally, we demonstrate the improvement of the quality of graphene grown on thus prepared foils through spectroscopic and carrier transport measurements.