  We examine and compare the gravitational lensing, in the strong field limit,
for the spherically symmetric string-inspired Euler-Heisenberg black holes,
characterized by additional parameters $Q^2$ and $\alpha-\beta$, representing
magnetic charge and coupling constant, respectively. Our analysis reveals a
reduction in the photon sphere radius $x_{ps}$, critical impact parameter
$u_{ps}$ and angular position $\theta_\infty$ with increasing magnitude of
$Q^2$ and $\alpha-\beta$. Consequently, the value of these quantities is
consistently lower than that of its GR equivalents. Further, the ratio
$r_{mag}$ of the flux of the first image to all others decreases with $Q^2$ and
$\alpha-\beta$. Unlike Schwarzschild black holes, string-inspired
Euler-Heisenberg black holes have a smaller deflection angle $\alpha_D$, which
decreases even more as $Q^2$ increases. Moreover, the time delay for Sgr A* and
M87* can reach up to $~11.302$ and $~17085.1$ minutes, respectively, at
$Q^2=0.1$ and $\alpha-\beta=-1$, deviating from Schwarzschild black holes by
$~0.194$ and $~293.6$ minutes which are not very significant. For Sgr A* and
M87*, we determine $\theta_\infty$ to range within $(23.81, 26.28)~\mu as$ and
$(17.89, 19.78)~\mu as$ respectively, with angular separations $s$ ranging from
$(3.33-5.67)~nas$ for Sgr A* and $(2.51-4.26)~nas$ for M87*. EHT bounds on the
$\theta_{sh}$ of Sgr A* and M87* within the $1\sigma$ region, bound the
parameters $Q^2$ and $\alpha-\beta$ as: for Sgr A* $0.29278 \le Q^2 \le
0.60778$ and for M87* $0 < Q^2 \le 0.08473$, but in both the cases we found no
bound on the parameter $\alpha-\beta$. We also estimate the parameters
$\alpha-\beta$ and $Q^2$ associated with string-inspired Euler-Heisenberg black
holes using the EHT observation results of Sgr A* and M87*.
