At first sight, option A looked quite OK to me.
Would appreciate if some one can explain the reason for picking up E, other than Responding to the recent uprising in downtown Detroit...

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In response to the recent uprising in downtown Detroit, residents quickly claimed that their trust in the mayor and the local government are being undermined by reports of political irresponsibility.
a. In response to the recent uprising in downtown Detroit, residents quickly claimed that
b. Responding to the recent uprising in downtown Detroit, residents quickly made the claim about wordier
c. When responding to the recent uprising in downtown Detroit, residents quickly make the claim about
1: meaning altered
2) make the claim is wordier than just claimd.
d. As a response to the recent uprising in downtown Detroit, residents quickly made the claim about
e. Responding to the recent uprising in downtown Detroit, residents quickly claim that
correct

on comparing A and E , E is more concise than A

A is wrong because the tenses don't agree. In A "residents quickly claimed that" claimed is past tense, but the next verb in the sentence is in the present tense.