In this paper, an adaptive inter-track interference (ITI) mitigating scheme is proposed for interlaced magnetic recording (IMR) with random frequency offsets. Recently, proposed IMR has a potential areal density capability gain over conventional perpendicular magnetic recording, as it involves writing tracks with differentiated linear densities in an interlaced manner, while suppressing the ITI efficiently during the reading operation via asynchronous ITI cancellation (A-ITIC). The A-ITIC estimates and subtracts the ITI contributions from its side tracks in the effectively synchronized domain via interpolation-filter-based relative timing adjustments. However, when the tracks are recorded with non-negligible random frequency offsets, the ITI response is averaged out, providing a weak estimate, and the A-ITIC-based bit error rate performance gain disappears. In order to compensate for these dynamic timing misalignments, an adaptive ITI mitigation scheme is proposed called an adaptive A-ITIC, where the ITI response is continuously updated via effective timing adjustments along the sector. Numerical evaluations using a micro-pixel-based magnetic channel model show that the legacy A-ITIC performs poorly for IMR with non-negligible random frequency offsets, whereas the proposed adaptive scheme compensates for most of the performance degradation by effectively tracing the relative timing shifts via adaptation measures.