Thulium- (Tm-)doped fiber lasers offer a broad emission bandwidth in the 2-µm region, providing the perfect basis to develop broadly tunable laser sources, e.g. for spectroscopic applications. Recently, a novel tuning principle for pulsed fiber lasers has been reported that is based on a fiber Bragg grating (FBG) array as a discrete spectral filter. This concept uniquely combines an unrivaled spectral freedom for tailored tuning ranges with a monolithic layout preserving the inherent advantages of fiber-integrated systems. In the present study, we investigate this discrete tuning method using a Tm-doped fiber laser in the spectral domain around 1950nm. While the laser emits linearly polarized light based on a polarization-maintaining (PM) resonator, we also examine the possibility of using standard FBG arrays inscribed in non-PM fiber. In order to highlight the prospect for tunable high-power operation, the tunable seed laser is implemented in a master oscillator power amplifier (MOPA) configuration scaling the average power to about 28W. With a tuning range of up to 76nm, the emission characteristics of the system are investigated showing pulse durations down to 11ns and a very good spectral signal contrast with narrow linewidth.