Ok, step-by-step ;-)
1.) List modules loaded on your client, when tinycore started and maybe even started rdesktop one time (for example via usb stick)
$ lsmod
2.) Note all modules (shouldn't be too much for a bare boot, e.g. there are loop, squashfs, ramzswap, ...), replace underscores with hyphens
3.) Unpack tinycore.gz to a temp folder
mkdir /tmp/unpackedtc
cd /tmp/unpackedtc
zcat tinycore.gz | sudo cpio -i -H newc -d
4.) In your remaster folder, where you extracted tinycore.gz, search for all modules except for those listed before under 2.)
find /tmp/unpackedtc/lib/modules -type f -name *.ko.gz ! -name ramzswap* ! -name loop* ! -name squashfs* -exec sudo rm -f {} \;
As you can see, he won't delete the modules ramzswap, loop, squashfs, ... (! = won't, * = .ko.gz), put your other modules right into that list.
5.) Search for other "big" unneccessary files and remove them manually and carefully
find /tmp/unpackedtc -size +50k
(/usr/bin/aterm, /usr/bin/zsync, ... )
Be careful with libraries, they might be needed somewhere, Xvesa as well
Install rdesktop and check for it's dependencies like
ldd /usr/local/bin/rdesktop
6.) Repack your tinycore.gz and you're done!