Step 1: Understand the situation.
Under the Code of Civil Procedure, 1908, while reading the pleadings the court finds some statements that are unnecessary and likely to prejudice or delay a fair trial. We must find what the court may do.
Step 2: Recall the relevant rule.
Order VI Rule 16 of the CPC gives the court power to strike out pleadings. It covers matter that is unnecessary, scandalous, frivolous, vexatious, or that tends to prejudice, embarrass, or delay the fair trial of the suit.
Step 3: Apply the rule to the facts.
The averments here are unnecessary and may prejudice or delay the trial. This fits Order VI Rule 16 perfectly, so the court can order them struck out.
Step 4: Note the timing.
An important point is that this power can be used at any stage of the proceedings. The court is not limited to acting only before the trial starts.
Step 5: Eliminate the wrong options.
Option A (amend only after trial begins) wrongly limits the timing. Option B (reject the plaint entirely) is too drastic, since only the offending pleadings need removal, not the whole plaint. Option D (ignore without any order) is wrong because the court acts through a proper order.
Step 6: Confirm the right answer.
The court strikes out such pleadings, and it may do so at any stage. That matches option C.
Step 7: Final answer.
\[ \boxed{\text{Strike out such pleadings at any stage of proceedings.}} \]