How to attenuate a (seemingly) overdriven VGA signal
Yes, you caused impedance mismatch when you connected the \$100\;\Omega\$ resistor in series with the RGB signals.

Most likely your output signal is larger than \$0.7\;V\$, which is the maximum specified signal voltage for the RGB lines.
Your solution for this situation would be an L-pad attenuator on the three signal lines. You don't need a more complex passive attenuator for this application, because signal travels only in one direction.

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Your source (\$R_s\$) has an impedance, in this case its \$75\;\Omega\$.
The load has the same impedance (the display). If you insert only one resistor in series with the signal line, then the impedances will be mismatched, signal reflection will occur, hence the ghosting.  

The best would be if you could open a fully white screen on one of the computers and measure the voltage on the RGB lines with an oscilloscope, and if its larger than \$0.7\;V\$ then design the attenuator accordingly.
For example, if your output signal is about \$0.9\;V\$, then you can calculate the attenuation in decibel with this:

\$\hskip6cm\$ \$20\cdot\log\cfrac{0.9\;V}{0.7\;V}=2.1829\;dB\$

If you want to calculate the resistance values from the dB value, it will look like this:


\$\hskip5cm\$ \$R_1=Z_s\cdot\left(\cfrac{10^\cfrac{2.1829\;dB}{20}-1}{10^\cfrac{2.1829\;dB}{20}}\right)\$

\$\hskip5cm\$ \$R_2=Z_s\cdot\left(\cfrac{1}{10^\cfrac{2.1829\;dB}{20}-1}\right)\$


It turns out, \$R_1=16.\dot6\;\Omega\$, and \$R_2=262.5\;\Omega\$.
The closest available resistor values are \$16\;\Omega\$ and \$270\;\Omega\$.
If you still experience ghosting problems with these values, then you should use trimmer potentiometers. The power doesn't exceed \$10\;mW\$ in this application so it should be safe to control the signal itself.

Here's the schematic of the solution:



Sources:

http://www.electronics-tutorials.ws/attenuators/attenuator.html
http://www.electronics-tutorials.ws/attenuators/l-pad-attenuator.html