In preparation for the forthcoming High-Luminosity phase of the Large Hadron Collider, the ATLAS experiment is working on major upgrades to its detector systems. A key component of these upgrades is the replacement of the current Inner Detector with the all-silicon Inner Tracker (ITk). The ITk consists of a Pixel Detector close to the beamline surrounded by a Strip Detector, which is made up of silicon strip modules. The silicon strip modules are operated at a bias voltage of up to 500V to ensure a 10:1 signal-to-noise ratio at the end of the ITk's lifetime. In such modules it is crucial to detect early breakdown, where current increases exponentially with increasing bias voltage below the 500V threshold. This contribution presents results from an irradiation campaign to investigate potentially beneficial effects of gamma irradiation on modules showing an early breakdown after gluing. Modules were exposed to an ionizing dose of 11 krad, corresponding to the dose accumulated after one week of operation in the HL-LHC. Preliminary findings suggest a discernible improvement in the breakdown voltage. These results mark a significant step towards establishing a reliable pattern of component recovery in the earliest stages of detector operations.