There are several ways to do this - depending on what you can do and/or what are your constraints. I'll use to describe the methods the last version of XnView MP (which by the way has also a Linux version), the DAM with which I'm most accustomed and, at least for me, has the most features which I need in this area:

1. Show files (recursive)

If this works, it is the quickest, simplest solution. XnView MP has multiple monitor support and a very powerful browser - it can build very fast the thumbs (near real-time) and you can set up them to show you at any size you want. Hence if you choose the most scalable compression available for thumbs (that is WebP) and an good size for your thumbs (eg. 300x200) - both settings are to be found in Tools | Settings | Database - then the only problem is to find a way to quickly navigate/scan the folders.

Here you have more options: - the simplest way: click on each folder and look. But this can be tedious. - go to the root of the 'suspect' folders in the Folders pane, right click on it and chose 'Show all files (recursive)' - this will show you all files from all subfolders in a single view. You can then sort them by date/name/etc. and have a look. If there are some photos which are almost the same (for ex. a result of a burst shot) you have Tools | Compare which will visually compare the selected files for you.

2. Printing with Captions

If you can do an index print (as you said) you have a lot of options here. For the selected files you can go to File | Print and there you have a lot of options (Pictures Collection, Thumbnails, Single and a bunch of variables to insert in the Caption area of picture). Explore it.

3. Adding info in Border/Image

Using Tools | Batch Convert you can add a wealth of info on image. Select some files and play with Tools | Batch Convert - pay attention especially at Actions tab where you can add a bunch of Batch Processing actions to your selection. Be sure that the output format is a non-lossy one (for ex. choose PNG or TIFF).

In the Actions tab, you can optionally choose Canvas Resize action in order to add a (white?) border around on which to print the desired info - see the settings of this action in the GUI (you have the preview of the result in the right side of the screen).

After that add on this border or straight on the pictures any text you want: add the 'Add Text' action and set up the color (faint yellow), the opacity and the text size you want. The only not-so-obvious thing here is the button for the fields from which you can insert the file name and/or other infos. It is pressed in the screenshot bellow:

In this way, you can batch write anything you want. You can also save these actions/settings (called 'Script' in XnView MP's terminology) - the Save button is on the left-bottom corner of the GUI to use them when you wish.

Also, you can choose an appropriate font to be easy to read and small in size (eg. Tahoma on Windows).

This small border can be hidden under the frame of your print and/or cut down when it will be sent to the client.

OTOH, knowing that you print at 300dpi you can print that info directly on the picture with a small font visible only at 100% zoom of a 600dpi scan.

4. You aren't allowed to fiddle with the print - Search by Content

IF you cannot/don't want to alter the print then you can simply scan the print put it in a newly created folder called eg. 'myNewScan' and go to Tools | Search Similar Files.. and there add the 'myNewScan' folder together with the root folder of your 'suspect' (candidate) files, choose as Method 'Similar picture content' move the slider somewhere near to 90-100 and go for a sleep, walk etc. The method can be very slow (obviously) and it can give false positives. It depends on you to tweak it.

5. Collaborate with your partner - Special Folders, Tags, Colors etc.

Why you cannot collaborate with your partner? (Yeah, I know, sometimes is quite impossible...)

Give her the same program (XnView MP works on LAN - ask on forums how to setup it) and tell them "what you print mark it with the "!!Printed" keyword/category or with the Yellow color, or whatever..."