Industrial gas turbines commonly use lean premixed swirl stabilized combustors that are prone to thermo-acoustic instabilities. Combustor testing involves several steps ranging from atmospheric to high-pressure conditions. An open outlet boundary condition is maintained for atmospheric tests commonly, whereas high-pressure testing involves complex exit boundary conditions, which change the reflection coefficient and can affect the nature of instability. Current work aims at studying how the change in outlet boundary affects the nature of instability due to changes in the exit reflection coefficient and acoustic mode shape inside the combustor. A laboratory-scale industrial swirl burner that uses partially premixed methane and air at atmospheric conditions is analyzed for this purpose. A constant area contraction ratio of 6.5:1 is maintained at the exit of the combustor while varying the inlet Reynolds number at a constant global equivalence ratio. Flame dynamics based on conditional phase averaged OH* chemiluminescence images and spatial Rayleigh index maps were used to compare different flow rate and exit boundary cases. The outlet contraction affects both the frequency and amplitude of the dominant thermoacoustic mode. The orifice plate at the exit reduces the outlet reflection coefficient leading to a change in acoustic mode shape inside the combustor. Overall, the instability amplitude is reduced considerably for cases with an orifice plates at the exit boundary compared to open exit boundary cases. The results show the importance of defining outlet boundary conditions as a parameter in combustion instability studies. Care should be taken while comparing and interpreting results from different facilities where outlet boundary condition is different.