Spatial heterogeneity is a general feature in planetary weather and climate, due to the effects of planetary rotation, heat distribution, land-sea distribution, fluid motion instability, etc. For 1:1 tidally locked (or called synchronously rotating) habitable planets around M stars, 3D global climate model simulations show that on the evening terminator (east of the substellar region) there are more water vapor and clouds than that on the morning terminator (west of the substellar region). This is due to the combined effect of coupled Rossby and Kelvin waves and equatorial superrotation. Using the Planetary Spectrum Generator (PSG), we calculate the differences in transmission spectra between the morning and evening terminators of the tidally locked terrestrial planets. We find that the transmission atmospheric thickness on the evening terminator is always larger than that of the morning terminator, due to the asymmetry in water vapor and clouds. This asymmetry signal is more significant for rapidly rotating planets having relatively low air masses than that for slowly rotating planets having relatively high air masses. However, this asymmetry signal is hard to be observed by the James Webb Space Telescope (JWST), because the magnitude of the asymmetry is much smaller than the instrumental noise.