Interest for high magnetic fields (>16 T) for applications in high energy physics (HEP) and fusion machines, requires the development of high current cables capable to withstand the large forces, mechanical and electromagnetic, experienced during manufacturing and operations. The critical current (Ic) of REBCO tapes depends on strain, magnetic fields, and operational temperatures. Understanding how these parameters affect the Ic of the conductor will be critical to develop robust high-current REBCO cables. However, there are limited reports on the strain dependence of Ic, in particular at high fields and elevated temperatures relevant for future high-field compact fusion reactor magnets. We present Ic of commercial REBCO tapes measured as a function of compressive and tensile strain (between-0.6% and +0.65%) at high magnetic fields (12 and 15 T) and different temperatures (within 4.2-40 K). Results at 4.2 and 20 K showed less than 5% reduction in the normalized Ic at high strain, while a stronger strain dependence was observed at 40 K. Samples tested at 12 T and 4.2 K showed similar strain dependence as 15 T and 4.2 K. In all tested conditions, the tape experienced reversible Ic reduction in both tension and compression. Finite element analysis was used to predict the residual thermal strain accumulated in the REBCO layer prior of testing to account for the effect of the cooldown. A method was also developed to account for the current sharing observed between the sample and the sample holder during the ramp of the current. Our results provide useful input for the development of high-field fusion and HEP magnets using REBCO conductors.