Why would a USB-C adapter have a pull-up resistor?
TL;DR

Adapters with Type-C male to Type-A female connections advertising a 56 kΩ resistor value are wrong. The resistor tells the Type-C downstream-facing port (DFP) whether the connected device is sourcing or sinking current. The presence of a female Type-A receptacle means that the adapter should use a 5.1 kΩ pull-down resistor to indicate that the device (whatever is plugged into the Type-A receptacle) is going to sink current.



I realized as I was researching this, that I have completely gotten it backward in the first version of this answer (now deleted), which is also what I think also happened in the case of adapters advertising the incorrect resistance values! Re-reading the specification several times, I've come to the conclusion that my initial approach was wrong. I've had to work with USB Type-C a little bit in a current project, and it's still pretty new to me. Anyway, this answer should now be correct.

USB Type-C introduces the concept of dual-role-power so devices, such as a battery, that can deliver (source) as well as accept (sink) current, can use a single connector.

A USB 2.0 type battery pack, for example has both a type-A female and a micro-B female connector:



The USB Type-C specifications (available at USB.org as "Universal Serial Bus type-C Cable and Connector Specification") explain different resistor values for determining whether a device is sourcing or sinking current.

Sourcing Table 4-24 (page 235):

Values used for pull-up \$R_p\$:



Sinking Table 4-25 (page 236):

Values used for pull-down \$R_d\$:





Page 85 specifically covers USB Type-C to USB 3.1 Standard-A Receptacle assemblies (the adapter shown in the question):


  Note 1. Pin A5 (CC) of the USB Type-C plug shall be connected to GND through a resistor \$R_d\$ (5.1 kΩ ± 20%).


If you're not careful (as I wasn't originally, and I expect the adapter makers also screwed up), you could look at Page 77 or 78 which show the specifications for USB Type-C plug to USB 3.1 and 2.0 Standard-A plugs. For these, the resistor is a pull up of 56 kΩ.