  Chance-aligned sources or blended companions can cause false positives in
planetary transit detections or simply bias the determination of the candidate
properties. In the era of high-precision space-based photometers, the need for
high-spatial resolution images has demonstrated to be critical for validating
and confirming transit signals. This already applied to the Kepler mission, it
is now applicable to the TESS survey and will be critical for PLATO. We present
the results of the AstraLux-TESS survey, a catalog of high-spatial resolution
images obtained with the AstraLux instrument (Calar Alto) in the context of the
TESS Follow-up Observing Program. We use the lucky-imaging technique to obtain
high-spatial resolution images from planet candidate hosts included mostly in
two relevant regimes: exoplanet candidates belonging to the level-one
requirement of the TESS mission (planets with radii $R<4~R_{\oplus}$), and
candidates around intermediate-mass stars. Among the 185 planet host candidate
stars observed, we found 13 (7%) to be accompanied by additional sources within
2.2 arcsec separation. Among them, six are not associated to sources in the
Gaia DR3 catalog, thus contaminating the TESS light curve. We provide upper
limits and probabilities to the possible existence of field contaminants
through the sensitivity limits of our images. Among the isolated hosts, we can
discard hazardous companions (bright enough to mimic a planetary transit
signals) for all their planets. The results from this catalog are key for the
statistical validation of small planets (prime targets of the TESS mission) and
planets around intermediate-mass stars in the main-sequence. These two
populations of planets are hard to confirm with the radial velocity technique.
Our results also demonstrate the importance of this type of follow-up
observations for future transit missions like PLATO, even in the Gaia era.
