In a 2007 note on ArXiv, it said:
String theory unifies all interaction but provides a perturbative background dependent formulation which violates general covariance.
However, another 2012 paper on ArXiv said that:
Instinctively, one identifies the constraint of the geometry being asymptotically AdS as a background and concludes that AdS/CFT is background dependent by construction. However, it has been argued that the situation is different...
...If the AdS/CFT conjecture is true, background independence of string theory could be proven, following this argument.
However, as we know, our universe is not AdS-like, but more similar to dS spacetime. The author also mentioned this in Sec.4.2.2:
The superselection sector of AdS/CFT is not the one we are living in since the cosmological constant was measured to be positive. If there were a duality to string theory in asymptotic de Sitter spacetime, a vacuum solution with positivecosmological constant, this would be a much more realistic model. This is being studied, see for example . Unfortunately, this has not been achieved yet for technical reasons.
Nevertheless, even in an AdS universe, the problem still exists:
The major problem is the lack of an actual proof of the conjecture...Part of the problem is also the AdS part of the duality being ill-defined. String theory can be defined perturbatively, but as argued before this cannot be the fundamental definition, which is still lacking. Attempts to define it with e.g. string field theory have not succeeded yet.
So, does string theory violate general covariance or not? Or we are just still not sure about it?