Guo–Schlosser's supercongruence for primes congruent to 2 modulo 3

Let $(x)_0=1$ and $(x)_k=x(x+1)\cdots(x+k-1)$ denote the Pochhammer symbol. Guo–Schlosser's supercongruence. For every prime $p\equiv 2\pmod{3}$, one has

$$\sum_{k=0}^{(p+1)/3}(6k-1)\frac{\left(-\frac{1}{3}\right)_k^4(1)_{2k}}{(1)_k^4\left(-\frac{2}{3}\right)_{2k}}\equiv p\pmod{p^3}.$$

This is a supercongruence for a truncated hypergeometric series. It was proposed by Guo and Schlosser and later confirmed by Jana and Kalita, so it is solved.