"Compromise" here means "weaken or harm by being exposed to, affected by or accepting standards that are lower than is desirable". In your sentence, the meaning is "the ratings may become, or be regarded as, less rigorous, less reliable or less authoritative as a result of..."

This may represent a case in which over-reliance by market participants on a few rating agencies could reinforce practices that compromise the integrity of their ratings. In this context it means that by over relying on what they are doing it could "hurt" or "skew" their ratings. Think like this. You and I have a TV show but because we were advertising to the wrong people we caused a lot of people to STOP watching our show. We "COMPROMISED" something good and by doing so we made things worse.

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I guess :put in a risk :jeopardize