I'm glad you asked:
Fire up your oscilloscope and make sure the channel trace is DC coupled. Install a BNC T-junction on your function generator and connect both your oscilloscope and the meter under test. The meter should be set on the ACV range.
Feed a 5Vpp sine wave at 100Hz to both of them, with 0 DC offset.
Note that TRMS is showing correctly on both oscilloscope and meter, namely 1.77VDC.
Now, increase the DC offset to 1V. The 61E will show something like 1.7016V, while the oscilloscope will display TRMS at about 2VDC.
With 2V DC offset, the 61E shows 1.706V instead of TRMS 2.63V. With 3V offset, it displays 1.705V instead of 3.46V TRMS, and so on.
If your oscilloscope doesn't show TRMS, work it out with the formula for a sine wave with a DC offset.
If you can, get your 71E out of the cobwebs and it will show the correct TRMS with any offset in the AC+DC mode.
This holds true, for any function, as long as the crest factor is kept below 3.