Peeking at the long term chart[1], I don't think 0.1% is notable. In Oct 2018, it bounced around ~1% under the peg for most of 2 months. Then in Dec 2018, it bounced around 1-2% over the peg for 2 months. A similar swing happened in Apr-Jun 2017. I'm actually surprised, I've never looked at this chart before and I didn't expect to see swings of several percentage points. But at any rate the current 0.1% is pretty tame in comparison and I'm sure it's just the cost of moving money to arbitrage.
If you zoom in to the first time period I mention (Oct 2018), and inspect visually, it was strictly under $1 for nearly two months. Right after that it was strictly over $1 for nearly two months. That's if you trust that site's data of course.
Remember this is the price on the secondary market, and these are just random people who see the price and then shuffle money around so they can buy a dollar for 99.9 cents. Anyone can do it (if you can stomach exposure to USDT of course). So if the system is working properly the price should generally hover within $1 plus or minus the cost to move money, but there's nothing keeping it at exactly $1.000000.
coinmarketcap/coingecko are generally not very reliable for evaluating the stability of stablecoin pegs
most liquidity tends to aggregate on dexes like Curve, which is also where you could have seen the whole LUNA/UST debacle play out in real time as large actors swapped out of UST into USDC/USDT/DAI
[1]: https://coinmarketcap.com/currencies/tether/