A tor2web proxy is just like a standard piece of network infrastructure. The proxy doesn't inspect or modify content; it just relays messages back and forth.

Below a legal analysis from a US law perspective

DMCA requests

17 USC 512(a) (part of the DMCA) says:

A service provider shall not be liable ... for infringement of copyright by reason of the provider's transmitting, routing, or providing connections for, material through a system ... operated by or for the service provider, or by reason of the intermediate and transient storage of that material in the course of such transmitting, routing, or providing connections, if --

1. the transmission of the material was initiated by or at the direction of a person other than the service provider;

2. the transmission ... is carried out through an automatic technical process without selection of the material by the service provider;

3. the service provider does not select the recipients of the material except as an automatic response to the request of another person;

4. no copy of the material made ... is maintained ... in a manner ordinarily accessible to anyone other than anticipated recipients [or] for a longer period than is reasonably necessary for the transmission...

5. the material is transmitted ... without modification of its content.

512(b) extends the immunity to "generally accepted industry standard" caching.

(The DMCA takedown notice procedures you may have heard of are part of 512(c) and only apply to services that store copies of material.)

Other copyright requests

Tor2web.org does not provide, select, or host the content available on Tor hidden services that are accessible through the Tor2web.org service, just as other Internet Service Providers do not provide, select, or host the content accessible on the Internet by their users. Like other ISPs, we are protected under United States law by 47 U.S.C. § 230 and 17 U.S.C. § 512(a), among other laws. We, like other ISPs, have no obligation to block access to sites that we do not host, even if those sites themselves may host material that other parties assert their some legal right.

For more information, see the Tor legal FAQ.