Before revision:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose  \ \et  2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.
After revision:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose  \ \et al, SICOMP, 42(4):1720--1736, 2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.