The interfacial Dzyaloshinskii-Moriya interaction (DMI) plays a crucial role in chiral domain wall (DW) motion, favoring fast DW velocities. We explore the effect of interface disorder on DMI and DW dynamics in perpendicular magnetized Ta/CoFeB/MgO thin films. Light He+ irradiation has been used to gently engineer interface intermixing on a scale of 0.1 nm. We demonstrate that a slight modification of the Ta/CoFeB interface leads to an increase of the DMI value accompanied by an enhancement of DW velocity in the flow regime. Using micromagnetic simulations based on granular structures, we show that the enhancement of DW velocity is mainly related to an increase in the distribution of magnetic parameters related to the interface. We further infer that the DMI modulation is related to the asymmetric disorder induced by irradiation leading to alloying with the Ta buffer layer. Understanding the role of disorder is therefore crucial for the design of future devices where post-growth interface alloying can be used to finely tune the DMI.