Wavelength tunable mode-locked fiber lasers have highly potential applications in precision spectroscopy, nonlinear microscopy and photonic sensing. Here, we present a compact and thermal-sensitive reflective Lyot filter and utilize it for all-polarization-maintaining efficiently wavelength-tunable Er-doped carbon-nanotube-mode-locked laser for the first time, to the best of our knowledge. The output wavelength of the laser can be tuned from 1544.46 nm to 1572.71 nm, with a wide tuning range of 28.25 nm, and a remarkable tuning efficiency of 0.589 nm/°C, when the angle-spliced fiber is only 8.2 cm and the free spectral range of the filter is 31.32 nm. Dual-wavelength mode-locking is also achieved at boundary temperatures when increasing the pump power. Due to its compact size and reflection configuration, the proposed reflective Lyot filter is promising for realizing highly efficient wavelength tuning and multiwavelength generation in all-polarization-maintaining fiber lasers where reflective filters are needed.