In my opinion , No , You Can not Claim Input Tax Credit, because as per section 16(2) of the CGST Act, to claim Input tax credit , Invoice and Goods or services must receive by the Business entity, in your Case services are received by employee , also Invoice may be in the name of employee , only you are paying , So You Can not claim ITC .
Although there is no GST on education services, however even if it has been charged, take invoice in the name of firm and if you think that it is for your business purposes, you can avail. it is similar like if any training is availed. Regards