The faithful have worn away the paint on the foot of this statue of St. Thérèse of Lisieux at St. Michael's Cathedral with their tender touches and reverential kisses.
Catholics (and Orthodox) do not worship statues. We do make use of images of Our Lord and His saints and martyrs. Leontius the Hierapolian explains:
...I do reverence to the image of Christ. Not to the substance of wood and paint - that shall never happen... But, by doing reverence to an inanimate image of Christ, through Him I think to embrace Christ Himself and to do Him reverence... We Christians, by bodily kissing an icon of Christ, or of an apostle or martyr, are in spirit kissing Christ Himself or His martyr.
The flattened toes of the bronze (!) statue of St. Peter in St. Peter's Basilica similarly attest to the power of pilgrims' kisses.