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We discuss the modification of the properties of the tetraquark-like$T_{cc}(3875)^+$ and $T_{\bar c\bar c}(3875)^-$ states in dense nuclear matter.We consider the $T_{cc}^+$ and $T_{\bar c\bar c}^-$ in vacuum as purelyisoscalar $D^{\ast} D$ and $\overline{D}{}^{\ast} \overline{D}$ $S$-wave boundstates, respectively, dynamically generated from a heavy-quark effectiveinteraction between the charmed mesons. We compute the $D$, $\overline{D}$,$D^*$, and $\overline{D}{}^{*}$ spectral functions embedded in a nuclear mediumand use them to determine the corresponding $T_{cc}^+$ and $T_{\bar c\bar c}^-$self energies and spectral functions. We find important modifications of the$D^{\ast} D$ and $\overline{D}{}^{\ast} \overline{D}$ scattering amplitudes andof the pole position of these exotic states already for $\rho_0/2$, with$\rho_0$ the normal nuclear density. We also discuss the dependence of theseresults on the $D^{\ast} D$ ($\overline{D}{}^{\ast} \overline{D}$) molecularcomponent in the $T_{cc}^+$ ($T_{\bar c\bar c}^-$ ) wave-function. Owing to thedifferent nature of the $D^{(*)}N$ and $\overline{D}{}^{(*)}N$ interactions, wefind characteristic changes of the in-medium properties of the $T_{cc}(3875)^+$and $T_{\bar c\bar c}(3875)^-$, which become increasingly visible as thedensity increases. The experimental confirmation of the found distinctivedensity-pattern will give support to the molecular picture of thesetetraquark-like states, since in the case they were colourless compact quarkstructures the density behaviour of their respective nuclear medium spectralfunctions would likely be similar. Finally, we perform similar analyses for theisoscalar $J^P=1^+$ heavy-quark spin symmetry partners of the $T_{cc}^+$($T_{cc}^{*+}$) and the $T_{\bar c\bar c}^-$ ($T_{\bar c\bar c}^{*-}$) byconsidering the $D^{*0}D^{*+}$ and $\overline{D}{}^{*0} D^{*-}$ scattering$T-$matrices.

Properties of the $T_{cc}(3875)^+$ and $T_{\bar c\bar c}(3875)^-$ (and their heavy-quark spin partners) in nuclear matter