Identifying Source of Periodic Artifact at Op-Amp Output
Note that this is an autozero amplifier (also called chopper stabilized) - many very low offset opamps work by periodically sampling the input offset and injecting a compensating offset to counter drift in the front end.  To do this there is an oscillator in the opamp together with a set of analog switches at the input.  This can result in clock feedthrough to the output as well as charge injection at the input pins.

Presumably this device is using 131kHz as the switching frequency.

I can't find any detailed information on the Maxim part but here is some info for an Analog Devices part that is probably similar:

Analog Devices Zero drift opamp

If you really need the low offset and drift then they are the best type of devices to use - you may need to Just limit your bandwidth and filter out the clock.

The bandwidth of the auto-zeroing is enough to encompass 1/f noise in CMOS opamps so they can be very low noise for frequencies below 1kHz, a region where CMOS opamps tend to have problems. 

If you can't filter out the clock noise see if you can use a conventional part - they will often have a worse drift and offset performance but you can get them better than 100uV offset.  You may also have to trade-off input bias current because bipolar input amplifiers are usually better than CMOS for this parameter.  Bipolar are usually lower noise as well. 

A related problem I have had with a similar Linear Technology part (LTC2051) is that the autozero circuitry can take a very long time to recover from overload when the output saturates - many milliseconds for a part with GBW of many MHz. This makes them unsuitable for any application that saturates as a normal part of its operation such as oscillators or threshold detectors.