The lines that appear can be controlled via a property of Patch objects called LineStyle.
One way to do this would be to find all the patch objects and then use the SET command to change the 'LineStyle' to 'none'.
In this particular case, however, the function TETRAMESH allows you to specify this property at creation of the plot.
For example:
d = [-1 1];
[x,y,z] = meshgrid(d,d,d);
x = [x(:);0];
y = [y(:);0];
z = [z(:);0];
X = [x(:) y(:) z(:)];
Tes = delaunayn(X);
tetramesh(Tes,X,'LineStyle','none')
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