People who buy the bitcoin ETF are not buying bitcoin. They are buying a product aimed at following the price of bitcoin. The ETF will hold the bitcoin, or derivatives based on it.
but when they sell all of their shares they have to buy more bitcoin to back more shares. eventually it will have an effect on the market with coins being removed from it.
Yes, assuming a fully BTC backed ETF (like a gold ETF backed by physical gold).
I think basically how it works, is that ETF fund buys X amount of BTC holdings, puts it in cold storage, and sells X amount of ETF shares in an IPO. The fund then trades like a share in the open market.
What ties the value of the ETF to that similar to the price of BTC, is the arbitrages buying and selling the ETF shares and BTC's to maintain a parity in value.
If they then want to sell more ETF shares, they will have to buy more BTC to back it. If people start buying up ETF shares on the open market raising its price, BTC has to be bought to increase the BTC price to match it. It's very likely a lot of derivatives are going to have to be used to try and maintain the ETF value to the underlying asset.
EDIT: If the price of BTC is $2000, and the ETF price is $3000, then the ETF can be short sold as alternative to rising the BTC price, but that doesn't come without risks either.
That probably makes the SEC nervous, as bitcoins market cap is still small and not that liquid. If it does get approved, it will probably come with a lot of conditions at the start.