  We investigate the absorption and production processes of this new state in a
hadronic medium, considering the reactions $T_{cc}^+ \pi, T_{cc}^+ \rho
\rightarrow D^{(*)} D^{(*)} $ and the corresponding inverse reactions. We use
effective field Lagrangians to account for the couplings between light and
heavy mesons, and give special attention to the form factors in the vertices.
We calculate here for the first time the $ T_{cc}^+ - D - D^*$ form factor
derived from QCD sum rules. The results are also obtained by testing widely
utilized empirical form factors. The absorption cross sections are found to be
larger than the production ones. We compare our results with the only existing
estimate of these quantities, presented in a work of J.~Hong, S.~Cho, T.~Song
and S.~H.~Lee, in which the authors employed the quasi-free approximation. We
find cross sections which are one order of magnitude smaller.
