Any resistor in the range 2.2k to 3.3k will probably be fine when connected to a 3.3V power supply.
However, the one from the through-hole pad should be 1k (as specified by the datasheet (Note: you DO NOT want to click on the datasheet link unless you are prepared to down even below the bottom of the rabbit hole)).
A bit more detail:
Electret capsules need some power in order to work because they often contain a small preamplifier circuit for the microphone. This is sometimes known as "plug-in power". The audio codec we use provides a suitable (low-noise) 2.5V voltage source to be used for this purpose. This voltage source is broken out to an unpopulated through-hole pad on revB2 capes (which we started shipping around October this year), so older capes will not have this option available. A 1k resistor from the 2.5V voltage source to the electret capsule is what is recommended by the datasheet.
As an alternative, you can connect a resistor in the range 2.2k-3.3k from the BBB's 3.3V supply to the electret capsule. This voltage source is more noisy than the one provided by the codec, therefore will give slightly worse noise performance.
Last note: if you will ever solder something on the board, especially if unexperienced with the soldering iron, you definitely want to solder on the bottom of the board, where there are no components, so that you do not risk damaging the SMD components on the board.