The finish looks to be a satin (or even low gloss matte). It is either oil based or oil modified polyurethane.

I would pick up a pint/quart of two options (yep...you will have to suck it up). I would choose a satin oil based (like minwax) AND a matte oil modified polyurethane (like Varathane or minwax). You will take your tins and you will use two different paint brushes (small brushes...you need precision here).

You will put down a LITTLE bit of finish of EACH ONE on different planks. You will let it dry (x 24 hours). Yes. I know. You are running out of time but I can't help you with that.

Check the COLOUR and the GLOSS level. Which ever finish offers the BEST match (both colour and gloss) will be your choice. You will then put down two - three coats (maximum 2 coats in 24 hours). You will hope against hope the landlord doesn't notice.

Or you can do the proper thing and hire a flooring professional to come in a do a small 'finish patch'. In essence you will hire someone to do this work for you.

And next time, please do NOT use tape over wood flooring finishes. Even low-tack painters tape can and will rip off the floor finishes (including some vinyl and laminate finishes as well as hardwood).