我的理解是这里的's代表has.  That has something to do with me.(这是我比较熟悉的形式） 和 that has got something to do with me是等价的。理由如下

 “What does her husband do?” “I think it has something to do with computers.” = “I think it's got something to do with computers.” [=it involves computers in some way]

然后，That has got something to do with me这句话就something 进行提问，变成That has got what to do with me.进一步 疑问词放在最前面，助动词紧随其后，变成what's that got to do with me. 请问老师，可以这样理解吗？