  The two-particle momentum correlation functions between charm mesons
($\mathrm{D^{*\pm}}$ and $\mathrm{D}^\pm$) and charged light-flavor mesons
($\pi^{\pm}$ and K$^{\pm}$) in all charge-combinations are measured for the
first time by the ALICE Collaboration in high-multiplicity proton-proton
collisions at a center-of-mass energy of $\sqrt{s} =13$ TeV. For $\mathrm{DK}$
and $\mathrm{D^*K}$ pairs, the experimental results are in agreement with
theoretical predictions of the residual strong interaction based on quantum
chromodynamics calculations on the lattice and chiral effective field theory.
In the case of $\mathrm{D}\pi$ and $\mathrm{D^*}\pi$ pairs, tension between the
calculations including strong interactions and the measurement is observed. For
all particle pairs, the data can be adequately described by Coulomb interaction
only, indicating a shallow interaction between charm and light-flavor mesons.
Finally, the scattering lengths governing the residual strong interaction of
the $\mathrm{D}\pi$ and $\mathrm{D^*}\pi$ systems are determined by fitting the
experimental correlation functions with a model that employs a Gaussian
potential. The extracted values are small and compatible with zero.
