1.楼主理解有误.
2.see作为感官动词,如果引导“see + 宾语 + 宾语补足语”结构,其宾语补足语如果使用动词,则在主动句中可以有三种形式：不带to的不定式（即动词原形）,现在分词和过去分词.
如：I saw him enter the room.我看见他进了房间.（强调主动兼完成）
I saw him entering the room.我看见他正在进入房间.（强调主动兼进行）
I saw him beaten by his father.我看见他被他老爸殴打.（强调被动）
3.此时如果把含有该结构的句子变为被动句,则只用使用不带to的不定式做宾语补足语的句子要加上to.
而如果是现在分词/过去分词做宾语补足语的句子,它们变为被动时,不能加to.
如上面的三个例句变成：
He was seen to enter the room.
He was seen entering the room.
He was seen beaten by his father.
4.该题主动句中使用了现在分词giving off做宾语补足语,所以变为被动时不能加to.