Arduino reduces the laser power
The first thing I would recommend is to log into your Amazon account and contact the seller. Ask them to send you product documentation.

If the seller is not able to provide any, then you could return the product for a refund or try to figure it out how it works.

According to this document: TTL Laser

TTL modulators emit 100% of their power when a TTL "0" (0 VDC) is input and less than 5% of their power when a TTL "1" (5 VDC) is input.

gre_gor's comment about trying a simple PWM sketch sounds like an excellent place to start.