Exchanges do have whats called "Know your transaction" (KYT) implemented.

You can think of it as an automatic system that checks the source of the funds. Did it come from a mixer? a gambling site? an address linked to a terrorist organization, or maybe a hack of another exchange? etc. How much of a risk is it? High, medium, low?

A transaction from a bridge or an unknown exchange would only raise suspicion if the original funds you deposited to the bridge, were suspicious for example, or if the crypto platform has been involved in something shady.