When you send a lot of ETH or USDT to a big exchange like Kraken, do they care if its come from a smaller non kyc exchange like Blofin? Do they care if it came from a bridge?
Exchange already have their own check's mechanism and the only time you could run into a problem with exchange is when the volume of the money is higher than your kyc level, this could trigger the exchange to Carrie out suspension on your account until you upgrade your kyc verification, and also exchange suspect fund's that are from illegal sources so for that, try as much as possible to always avoid sending money from gambling and other coins mixing services that debts the status of the Bitcoin deposits.
Aside from all of that, if all your transactions are from clean source, I don't think you have anything to worry about on exchange deposit regardless of the level of the exchange or wallet you are sending the Bitcoin from, exchange not exceeding your maximum deposit limit puts you and your funds on a more positive note on an exchange.
So Note that large deposits always trigger's suspicion so to that makes sure to deposit all your Bitcoin in a much secured and below limit balance if you want to stay within the limit of you account on the exchange.
As long you wouldnt really be able to hit up the threshold then it should really be just that fine but on the moment that you do go past beyond it then you would be able to expect that there would really be checks that needs out or on the moment tor time that you will really be asked out for some verification if ever they have seen something odd with your transaction. Actually there's nothing to worry about if there's nothing that you do hide on where those funds came from. If it turned out that you are a whale holder then you could always prove it out that it do came from your own wallet but if this one talks about on gambling source of funds then there's really some rules or terms about that on which we do need to look upon.
These are only a couple of example with tons on the list. As long you dont put up yourself into these things then you should be just fine.