Hi,
C7 is not creating the noise. But it may cause to amplify it.
I assume it is common mode noise. Usually a difference amplifier attenuates common mode noise.
But only if R1 value = R15 value, which isn't the case here (here I assume someone didn't understand the circuit, but modifed it).
Adding C7 to R15 makes this even worse.
In your case you may disconnect C7. To further reduce common mode noise I recommend to use two 100nF capacitors.
Connect them at each side of C4 to GND.
Because this adds another 50nF to C4 and fc is close to mains frequency you may expect up to 10% less output voltage.
If you don't want this you may use 10nF capacitors
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By far the better solution is to correct the wrong R1 and R15 values. This brings improvement in almost any function of the circuit: noise, common mode input voltage range, symmetry, differential input voltage range...
Klaus