Cu(C$_8$H$_6$N$_2$)Cl$_2$, a strong-rung spin-1/2 Heisenberg ladder compound, is probed by means of electron spin resonance (ESR) spectroscopy in the field-induced gapless phase above $H_{c1}$. The temperature dependence of the ESR linewidth is analyzed in the quantum field theory framework, suggesting that the anisotropy of magnetic interactions plays a crucial role, determining the peculiar low-temperature ESR linewidth behavior. In particular, it is argued that the uniform Dzyaloshinskii-Moriya interaction (which is allowed on the bonds along the ladder legs) can be the source of this behavior in Cu(C$_8$H$_6$N$_2$)Cl$_2$.
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