Is it permissible to accept governmental financial aid for building a house, given that the salary exceeds the legally allowed limit, but salary statements were obtained showing an amount below the allowed limit due to not declaring some allowances, and knowing that the aid is not limited and does not detract from the right of others?

You must inquire with the responsible authority regarding the mandatory mention of the activity grant and the region. If they do not mandate it, then what you have done is correct. However, if they stipulate their mention, then the certificate must be amended to include them. You are not permitted to take what you do not deserve due to the non-fulfillment of conditions, as the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions."