Motivated by the recent observation of the tetraquark $T_{\mathrm{cc}}^{+}$ $$ {T}_{cc}^{+} $$ , we investigate the magnetic dipole moments of the possible single and double strange partners, $T_{\mathrm{QQ}\overline{q}\overline{s}}$ $$ {T}_{QQ\overline{q}\overline{s}} $$ and $T_{\mathrm{QQ}\overline{s}\overline{s}}$ $$ {T}_{QQ\overline{s}\overline{s}} $$ , with the spin-parity J P = 1+ by means of the QCD light-cone sum rules. To this end, we model these states as diquark-antidiquark states with different organizations and interpolating currents. The results of magnetic dipole moments obtained using different diquark-antidiquark structures differ from each other, considerably. The magnetic dipole moment is the leading-order response of a bound system to a soft external magnetic field. Therefore, it provides an excellent platform for investigation of the inner structures of hadrons governed by the quark-gluon dynamics of QCD.