The process of DNA transposition involves the binding, cleavage, and recombination of specific DNA segments (transposable elements, TE) and is catalyzed by special enzymes encoded by the TE transposases. REP-associated tyrosine transposases (RAYTs) are a class of Y1 nucleases related to the IS200/IS605 transposases associated with a bacterial TE known as repetitive extragenic palindrome elements (REPs). Although RAYT has been subject of numerous studies, where DNA binding and cleavage by RAYT have been confirmed for Escherichia coli, the molecular mechanism of DNA insertion has not been fully understood. In this work, it is demonstrated that surface plasmon resonance (SPR) biosensor technology combined with a system of DNA hairpin probes (mimicking the natural REP sequence) and short oligonucleotides (ONs) can provide a rapid and real-time platform for monitoring and quantification of RAYT activity. We utilized RAYT from E. coli (strain MG1655) as a model system, where we evaluated its activity towards both a natural REP sequence as well as REP sequences having modifications targeting specific features of the DNA crucial for the DNA binding and cleavage. The characteristics of the RAYT-DNA interaction obtained by means of the SPR approach were compared with the results of SDS-PAGE analysis.