Abstract: We discuss the modification of the properties of the tetraquark-like Tcc(3875)+ and Tc over bar c over bar (3875)- states in dense nuclear matter. We consider the Tcc+ and Tc over bar c over bar – in vacuum as purely isoscalar D*D and D*D S-wave bound states, respectively, dynamically generated from a heavy-quark effective interaction between the charmed mesons. We compute the D, D, D*, and D* spectral functions embedded in a nuclear medium and use them to determine the corresponding Tcc+ and Tc over bar c over bar – self-energies and spectral functions. We find important modifications of the D*D and D*D scattering amplitudes and of the pole position of these exotic states already for p0/2, with p0 the normal nuclear density. We also discuss the dependence of these results on the D*D (D*D) molecular component in the Tcc+ (Tc over bar c- over bar ) wave function. Owing to the different nature of the D(*)N and D(*)N interactions, we find characteristic changes of the in-medium properties of the Tcc(3875)+ and Tc over bar c over bar (3875)-, which become increasingly visible as the density increases. The experimental confirmation of the found distinctive density pattern will give support to the existence of molecular components in these tetraquark-like states, since in the case they were mostly colorless compact quark structures (cct over bar t over bar and c over bar c over bar tt, with t = u, d), the density behaviors of the Tcc(3875)+ and Tc over bar c over bar (3875)- nuclear medium spectral functions, though different, would not likely be the same as those found in this work for molecular scenarios. Finally, we perform similar analyses for the isoscalar JP = 1+ heavy-quark spin symmetry partners of the Tcc+ (T cc *+ ) and the T c over bar c- over bar (T*- c over bar c over bar ) by considering the D*0D*+ and D*0D*- scattering T matrices.