We study the interactions among a static quark-antiquark pair in the presence of dense two-color quark matter within lattice simulations. To this end we compute Polyakov line correlation functions and determine the renormalized color-averaged, color-singlet and color-triplet grand potentials. The color-singlet grand potential allows us to elucidate the number of quarks induced by a static quark antiquark source, as well as the internal energy of such a pair in dense quark matter. We furthermore determine the screening length, which in the confinement phase is synonymous with the string breaking distance. The screening length is a decreasing function of baryon density, due to the possibility to break the interquark string via a scalar diquark condensate at high density. We also study the large distance properties of the color singlet grand potential in a dense medium and find that it is well described by a simple Debye screening formula, parameterized by a Debye mass and an effective coupling constant. The latter is of order of unity, thus even at large density two-color quark matter is a strongly correlated system.