CRISPR-associated transposases (CASTs) repurpose nuclease-deficient CRISPR effectors to catalyze RNA-guided transposition of large genetic payloads. Type V-K CASTs offer potential technology advantages but lack accuracy, and the molecular basis for this drawback has remained elusive. Here, we reveal that type V-K CASTs maintain an RNA-independent, "untargeted" transposition pathway alongside RNA-dependent integration, driven by the local availability of TnsC filaments. Using cryo-electron microscopy, single-molecule experiments, and high-throughput sequencing, we found that a minimal, CRISPR-less transpososome preferentially directs untargeted integration at AT-rich sites, with additional local specificity imparted by TnsB. By exploiting this knowledge, we suppressed untargeted transposition and increased type V-K CAST specificity up to 98.1% in cells without compromising on-target integration efficiency. These findings will inform further engineering of CAST systems for accurate, kilobase-scale genome engineering applications.