Tax paid under rcm by a rent a cab service provider paying output tax @ 5% (i.e. ineligible for itc)

Dear colleagues,

There is a case where the concerned person is a "Rent a Cab" Service Provider. He is charging 5% output tax and hence ineligible to claim ITC on Input goods and services. He avails service from unregistered parties and had to pay tax under RCM  Now, the question is whether the Service Provider is eligible to claim ITC of tax paid under RCM? If not, can we claim refund of Tax paid under RCM??

Also, suggest a better alternative or way to deal with this..