Well, I was curious enough to google it and found a 10 year old "Ask A Bear" column from Backpacker Magazine. They say it's not a worry...
If you use dryer sheets in your clothes, the bear will smell that anyway, and probably associate that with "human", which they want to avoid. It's a chemical smell and not a food smell
Dryer sheets in your dryer making your clothes smell faintly nice to you, and a dryer sheet in your pack to keep your dirties from being overwhelming in the tent are two very different things to a bear. It's like a single berry somewhere in your tent vs. a whole berry forest stuffed into it. A bear absolutely tore through the tent and pack of a girlfriend of a girlfriend on JMT - the ONLY thing she ever had in that tent was a single dryer sheet. No food, no sunscreen, no toothpaste - just one dryer sheet.
Not enough to put her in danger - she was day hiking away from camp, and came back to find her tent shredded and flattened with a bear on top of it, rolling on it.
If you've ever backpacked in the Sierras, and specifically in Yosemite Valley, most bears there will almost automatically go after anything associated with "human" because they have been conditioned to expect to find food. They will break into a car if they can just *see* a cooler in it - even if they can't smell anything.
Regardless, you don't need to shoot a bear because it shredded your tent - black bear aren't dangerous unless cornered, protecting cubs, or occasionally when encountering single sleeping or perhaps injured humans when hyperphagic.
