What a unique find! We have never owned a 1937 Chevy truck grille with all of its clips in place. It was necessary to get photos before this assembly got away.
These clips (4 on each of the four sides) are actually an extension of the large stamped metal housing. Obviously, GM did not plan on the inside grill being removed more than one or two times which then might break these clips during bending. Certainly GM had no concern if the clips would break on a work truck over 75 years later during a restoration.
Thus, a recommendation: When removing the 1937 grille, gradually bend each of the 16 clips just slightly so none are given a more than needed straightening. Bending them back less when replacing a restored grille will lessen their chance of breaking. Good Luck!
The Complete Grille Housing (without grille)
NOTE: Visible clips on top and bottom
4 Clips Below Top Edge
Right Side of Housing
Clips on Left Side of Housing
Clips are Part of Sheet Metal Housing