  Optical surveys have become increasingly adept at identifying candidate Tidal
Disruption Events (TDEs) in large numbers, but classifying these generally
requires extensive spectroscopic resources. Here we present
$\texttt{tdescore}$, a simple binary photometric classifier that is trained
using a systematic census of $\sim$3000 nuclear transients from the Zwicky
Transient Facility (ZTF). The sample is highly imbalanced, with TDEs
representing $\sim$2% of the total. $\texttt{tdescore}$ is nonetheless able to
reject non-TDEs with 99.6% accuracy, yielding a sample of probable TDEs with
recall of 77.5% for a precision of 80.2%. $\texttt{tdescore}$ is thus
substantially better than any available TDE photometric classifier scheme in
the literature, with performance not far from spectroscopy as a method for
classifying ZTF nuclear transients, despite relying solely on ZTF data and
multi-wavelength catalogue cross-matching. In a novel extension, we use
`SHapley Additive exPlanations' ($\texttt{SHAP}$) to provide a human-readable
justification for each individual $\texttt{tdescore}$ classification, enabling
users to understand and form opinions about the underlying classifier
reasoning. $\texttt{tdescore}$ can serve as a model for photometric
identification of TDEs with time-domain surveys, such as the upcoming Rubin
observatory.
