In the assessment of damages and benefits for the opening of any street or alley, the commissioners, where part of the land to be laid out into that street or alley has been theretofore donated by any person for that street or alley, may appraise the value of the land so donated. Or in cases where such a donation is made after the filing of any petition in the circuit court praying that steps be taken to levy a special assessment for the opening of any street or alley, and after the making of the assessment roll as provided in this Division 2, the court may appraise, or may have a jury appraise, the value of the land so donated. The commissioners or the court, as the case may be, shall apply the value thereof, so far as the amount so appraised shall go, as an offset to the benefits assessed against the person making such a donation, or parties claiming under such person. Nothing contained in this section authorizes any person by whom such a donation is made to claim from the municipality the amount of that appraisement, except as an offset, as provided in this section. Where the assessment is only for the widening of any street which may have been theretofore donated either in whole or in part, to the public by the proprietors of the adjoining land, the commissioners, in their discretion, may make such allowance therefor in their assessment of benefits as seems to them equitable and just. But in either such case the commissioners shall state in their report the amount of that allowance, and the allowance shall be subject to review, as the court shall direct.