Tomcat was blocking DELETE methods for me because of my CORS filters.
I needed new filters registered in my web.xml file. Here's an example of a very permissive one:
<filter>
<filter-name>CorsFilter</filter-name>
<filter-class>org.apache.catalina.filters.CorsFilter</filter-class>
<init-param>
<param-name>cors.allowed.headers</param-name>
<param-value>Accept,Accept-Encoding,Accept-Language,Access-Control-Request-Method,Access-Control-Request-Headers,Authorization,Connection,Content-Type,Host,Origin,Referer,Token-Id,User-Agent, X-Requested-With</param-value>
</init-param>
<init-param>
<param-name>cors.allowed.origins</param-name>
<param-value>*</param-value>
</init-param>
<init-param>
<param-name>cors.allowed.methods</param-name>
<param-value>GET, POST, PUT, DELETE, OPTIONS, HEAD</param-value>
</init-param>
</filter>
<filter-mapping>
<filter-name>CorsFilter</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>