Is there a proper way to eject a USB thumb drive from an iPad?

Not necessarily. Depending upon the USB storage device, to avoid corruption, you may need to be a little more cautious...

Apple hasn’t chosen to include a safe-eject option in iOS/iPadOS. There reasoning and design decisions for this (or any feature) are known only to Apple Engineering.

Providing your attached USB Storage device does not employ write-caching, you should be able to disconnected a USB Storage device wherever the device is not being actively written to; it follows that you should ensure that a file-write has completed prior to a device disconnect.

In more detail:

The type of flash storage device that you are using will have significant impact on “safe dismount” from your iPad. Simple flash storage devices can be dismounted provided that an active write isn’t occurring. More complex devices are a completely different proposition…

The technical reason for caution is write-caching - this being a feature of the USB Storage (in this case SSD) device.

For most desktop computers, it is possible to configure an externally attached storage device either for performance (i.e., uses write-caching) or for Quick Removal. This determines how and when information is “written” to non-volatile storage.

When configured for Quick Removal, information from the host computer is written immediately to the storage medium. This has the advantage that you may disconnect the storage device from the host computer, without risk of corrupting the file-system, at any time that data is not being actively transmitted to the storage device. Whilst being a completely valid and useful method of managing data storage, for reasons beyond the immediate scope of this description, this method is less efficient and slower.

Alternatively, when write-caching is enabled, information from the host computer is “cached” in separate (high performance) volatile storage within the storage device - and when sufficient information has been received, a “block” of data is written in single write-cycle. Whilst being faster and more efficient, this method comes with the penalty of the host computer having to notify the storage device of a impending device-disconnection before it is disconnected. This warning ensures that the storage device will flush any pending data from its volatile cache-memory to non-volatile storage - and in so doing sets a “clean switch” on the flash filesystem and signals to the computer that it is safe to disconnect.

A drive configured for write-caching, upon connection to a host computer, is checked for the “clean switch”; if present, the storage device is “mounted” and made available to the operating system. By contrast, if the “clean switch” is not detected (this will occur if the storage device was disconnected prior to being notified of a “dismount”), the filesystem must be assumed to be potentially corrupt; pending data within the write-cache may not have been written to the drive.

So, the relevance of this to iPad is simple. iPad does not fully support devices that implement write-caching. iPadOS lacks the ability to inform the storage device of imminent disconnection of the storage device from the USB bus. iPad also lacks capability to detect and scan/repair corrupt storage devices.

In summary, now that you [hopefully] understand both the cause and effect, you will now understand that you can only reliably use USB storage devices that can be configured for Quick Disconnect operation - this having major significance to non-corruption of the filesystem and reduced data throughput.

The only “safe” dismount is to fully shut down the iPad before disconnecting.

I hope this information and insight proves to be helpful.

Yes, as long as the files have transferred, you just remove it. There's no "eject" like there is on a Mac.

Regards.