Screen Door...???

i've been processing a whole bunch of old & very old family pictures
that my mother let me scan,
and while correcting the colors of Evil Kodacolor & Kodachrome prints,
and adjusting contrast, filling in cracks & dust spots and so on...

i've found it prudent to reduce them down before posting them on
Flickr ( Account: Chrstphre )
And Often; after reducing them with Graphic Converter, they will take
on a decidedly Gridular, or Screen Door appearance...??? As if i were
looking at them through a screen door...!

i've pretty much decided that this is due to some weird algorythmic
anomaly that could be remedied by reducing them at a quantified
pro****tion that is calculated with original size & desired size in
mind...

i have every confidence that i could figure this out on my own with
lots of deep thought, and plenty of trail & error, but it might be
quicker if i wait 24 hours and let one of you genius' tell me what the
formula is...???

Thanx!