Some form of chromatography should useful. The simplest in terms of equipment would be thin layer chromatography, but analytical HPLC or UPLC would give higher resolution of products and be more amenable to quantitation. Some work would be needed to find optimal conditions for the chromatography.

Try to directly check by HPLC/TLC, or do raction with a reactive smalll moecule, then check HPLC/TLC.

Quantification on an area% basis by reverse-phase HPLC with UV/Vis detection is typically used for quantification of reactive dye hydrolysis: I have used the former analytical technique to track hydrolysis of monofunctional sulphatoethylsulphone and dichlorotriazine reactive dyes. With the first type of dyes, I deliberately subjected samples of dye to prolonged heating with alkali to generate reference solutions that contained vinylsulphone (reactive form) and hydroxyethylsulphone (hydrolysed form) species. Hydrolysed dyes have similar absorption spectra to unhydrolysed dyes so at least selection of detection wavelength is straightforward.

Tracking hydrolysis with bi- or multi-functional reactive dyes is more complex given the potential for formation of several hydrolysed species, but identification with HPLC-MS is possible: for example, see Article Dimerised heterobifunctional reactive dyes. Part 1: characte...

and

Article Degradation studies of CI Reactive Blue 19 on biodegraded ce...

Another, albeit less commonly used, method for monitoring hydroysis is capillary electrophoresis coupled with a UV/Vis detector.

I would not recommend TLC, especially with silica plates, or even with paper. Because reactive dyes are sulphonic acid derivatives, they require highly polar mobile phases with silica plates to get them off the baseline and even then they do not tend to chromatograph well. Also, obviously TLC the technique only gives a qualitative indication without use of a densitometer.