What happens in the titration?

In acidic medium, potassium permanganate oxidizes oxalic acid.

The relevant reaction is: $2MnO_4^- + 5H_2C_2O_4 + 6H^+ \rightarrow 2Mn^{2+} + 10CO_2 + 8H_2O$

So, the titration must be carried out in an acidic medium, and usually dilute $H_2SO_4$ is used.

Why is $HCl$ not used?

Permanganate is a strong oxidizing agent in acidic medium. In presence of $HCl$, the chloride ion $Cl^-$ gets oxidized to chlorine gas.

The reaction is: $2MnO_4^- + 16H^+ + 10Cl^- \rightarrow 2Mn^{2+} + 8H_2O + 5Cl_2$

Thus, $HCl$ also reacts with $KMnO_4$, consuming permanganate and disturbing the titration result.

Check the options

A. gets oxidised by oxalic acid to chlorine
Incorrect. Oxalic acid is a reducing agent; it does not oxidize $HCl$ to chlorine.

B. furnishes $H^+$ ions in addition to those from oxalic acid
Incorrect. Acidic medium is required anyway; this is not the reason for unsatisfactory results.

C. reduces permanganate to $Mn^{2+}$
This is the closest correct statement in the given options. More precisely, chloride ion from $HCl$ gets oxidized, thereby reducing permanganate to $Mn^{2+}$ and causing error.

D. oxidises oxalic acid to carbon dioxide and water
Incorrect. $HCl$ is not an oxidizing agent here.

Conclusion

The titration gives unsatisfactory results in presence of $HCl$ because $HCl$ (through $Cl^-$) reacts with permanganate, reducing $MnO_4^-$ to $Mn^{2+}$.

Therefore, the correct option is: $\boxed{C}$